It's this one https://www.aliexpress.com/item/4000056606252.html
If you are comfortable adding a small piece of aluminum/copper in between the gap, then it's great. But if you like something that just works then stay away from it.
It's really odd those Chinese manufacturers don't check these kind of things before manufacturing by the thousands...

Tried leaving it running with 100% load on all cores (cpuburn-a53). It stabilizes at 71C after about an hour. Damn hot to the touch but no clock throttling.
If 100% load was a 24/7/365 thing, then I would definitely go with a fan but being an intermediate condition it is fine.

bitcoind and lnd doesn't even seem to mind the cpu being kept busy :-)

Have fun playing :-)
I need to get a second one now that I allocated mine to run a bitcoin node 

There's 22C ambient. No airflow but it's in 'the open' (i.e. unrestricted convection) in the corner of an office:
http://too-hot.dk/storage/temp/raspi_case.jpg
Showing 52C after a couple of hours - haven't seen it higher than that yet. Dropped to 51C after taking the image.

You can even tell I'm currently using a rotary disc on the thermal  image
http://too-hot.dk/storage/temp/thermal.jpg

I was expecting about 50C given a sizeable heatsink with good thermal interface. A bit of forced convection will really help, but I want a completely quiet solution and 50C is totally fine :-)

Oh, by the way. I removed the anodized surface of the area of the heatsink that evenually contact the cpu. Anodized aluminum is a really good insulator of both electricity and heat. Probably doesn't matter much at this relatively low thermal densitity though. But we recently had an issue at work with a heatsinks delivery that was inadvertently anodized at the contact area where we transfer in excess of 100W/cm2 from a power tranasistor. This caused an increase in die temperature of more than 10C so we had to rework those heatsinks by milling the surface.

Received one of the cheap cases, the one with ribs. And as DaveF suspected, there were no contact between cpu and heatsink. There were about 1mm air gap 😕.
I cut a small piece of 1mm aluminum and fitted it with heatsink compound, which turned it into an ON OK solution 🙂.
Raspiblitz running at about 50C now.

Edit: Fixed typo.

I can't say for sure as I had some troubles with the last part of the sync and did some experiments etc. But at least, the first half of the blockchain (i.e. +100GB) was downloaded within the first day.
With optimum conditions (fast network and SSD drive) I believe a  clean sync should easily complete within two days on the RPI4B.

I now also got raspiblitz (Bitcoin + LND) up and running :-)
With the small passive heatsink temperature settles at about 68C with some open connections...


               RaspiBlitz v1.3  Blitz99
               bitcoin Fullnode + Lightning Network
        ,/     -------------------------------------------
      ,'/      CPU load 3.85, 3.75, 2.71, temp 68°C 154°F
    ,' /       Free Mem 3392M / 3906M  HDDuse 262G (95%)
  ,'  /_____,  ssh admin@192.168.0.164 d8.3MiB u25.8MiB
 .'____    ,'
      /  ,'    bitcoin v0.18.1 mainnet Sync OK 100.00%
     / ,'      Public xx.xxx.xxx.xx:8333 17 connections
    /,'
   /'          LND 0.7.1-beta wallet 0 sat (+400000)
               0/0 Channels 0 sat 4 peers

Yes it finished. Not without problems though 

I naively thought the blockchain would still just fit on my 250GB SDD but turned out I was about 20 gig short.
Then I moved the data to a larger 5400 rpm HDD which of course is awfully slow at sync'ing.

Then then project turned into a filesystem experiment. I re-formatted the 250GB SSD to a btrfs filesystem with zlib compression enabled and copied the blockchain back.
Even though the blockchain is poorly compressible it still compresses to about 80% i.e. freeing up sufficient space with some 10GB to spare after sync'ing was done.
Naturally, the compressed SSD is also significantly slower than uncompressed it is still much faster than the HDD. I guess I just need to order a new disk..

Now I'm fiddling around with raspiblitz to get some hands-on with lightning 

I ordered one of those china aluminium boxes - will see how it fits and whether the thermal interface can be done properly. But as mentioned, it is not really a huge problem. It will throttle down if it gets too hot and normally it won't even get that hot when just staying in sync.

There's also a great overview on cases/cooling here: https://www.martinrowan.co.uk/2019/09/raspberry-pi-4-cases-temperature-and-cpu-throttling-under-load/

Passive cooling i.e. natural convection does indeed require a really huge heatsink compared to forced air-flow cooling. To be effective you basically need the entire case to be a heatsink.

If you have the data it is fairly easy to calculate the temperature rise of a heatsink given the required power dissipation. Or at least getting a rough estimate.
It might be difficult finding data for a Chinese raspberry case, but let's say we want a heatsink to be 30C above ambient then you would need one with a thermal resistance of 3 degree C per watt at natural convection.
A random example of a heatsink specified for 3 C/W @ natural (not suitable for RPI but just to provide a hint about size) : https://www.digikey.com/product-detail/en/wakefield-vette/401K/345-1048-ND/340344
On top of this comes the thermal resistance in the interface between the chip and the heatsink, which adds to the temperature rise of the silicon. On the other hand, a lot of the power dissipation is caused by other chips on the RPI board than the CPU.
Sorry for blabbering. Just happened to be an electrical engineer doing stuff like that for a living 

Btw. I've plugged the RPI to my own LAN. It's sync'ing much faster again. Should be done sometime tomorrow :-)

Will try to order one or both of these 'cool'  cases from china. There are also options with fans but I really prefer passive cooling for something that is intended for 24/7 use.
https://www.aliexpress.com/item/4000056606252.html
https://www.aliexpress.com/item/4000095452880.html

I believe our ISP or other internet infrastructure has limited the throughput to my raspberry. Maybe someone thought +100GB/day is excessive for a single device 
The sync speed dropped significantly over night. So did CPU usage (and temperature). As far as I can tell, it's limited by the network as neither CPU or disk are loaded.

Screenshot:


But 45% done after about 20 hours are not bad either :-)

Heat management has been a major concern with RPI4. Unfortunately it's limited by technology. You only get a certain amount of MIPS per watt at a certain technology node. (btw. I used to work for Intel).
RPI4 manages it pretty well i.e. throttles down the clock when temperature exceeds 80C - it's built for operating at those temperatures (I hope). So you can either accept a slight decrease in performance at high workloads or add some heat dissipation capabilities. Or play around with under-volting/under-clocking if that's your thing.
I just got a small heatsink for now () which helps quite a bit. As you can see, it's at 60C with the moderate load. It still reaches 80C at full load though even with this heatsink (however, that requires more active processes than 'just' bitcoin).
There are a lot of cool cases for the RPI4 comming out, where the case is made of aluminum coupled to the CPU.

I left it sync'ing at my workplace. Will be interesting checking the status tomorrow to see if it could keep up the pace with the larger blocks.
I have a small passive heatsink on the cpu. It gets hot but sync'ing seems to be mostly a single core activity so it doesn't feel critically hot. Don't think it throttled down.
RAM usage was in the range of 1.3 GB when I checked, so don't go for the 1GB variant. It's running raspbian buster lite.
There's plenty of bandwidth to the external SSD through the super-speed USB connection. Also the gigabit LAN is no bottleneck.

Fyi. in case others are still interessted.

I got a fresh raspberry pi 4 Model B (4GB), connected a SSD using USB-SS and started sync'ing on a fast internet connecting.

After just a few hours I'm at 16% progress with >40GB downloaded and estimated 24 hours left.

Compared to older raspberries, the 4 are blazing fast