Most people ask this question without going into any details about what they want to use their PC for, which makes it difficult to offer a reply that can be helpful to the use case.
After saying this though, I would personally recommend a processor from the AMD Ryzen 2nd generation, or if you can wait a few months, the upcoming 3rd generation which will soon to be released. While Intel have had the IPC advantage for some time, as of right now that advantage is negligible and Intel really only has higher clocks speeds to keep them in front performance wise.
If processor security is a concern for you, then current Intel processors have a number of outstanding issues that still need to be addressed that make AMD a more secure choice. It's quite likely that Intel processors IPC will be degraded when addressing these security issues.
From a price and performance perspective, AMD wins hands down over Intel, and you'll get a better value product for your money.
If you're purely a gamer, then Intel currently offers a marginal advantage, but this will vary game to game and is largely dependent on your GPU more-so that the CPU. You'd actually be hard pressed to notice any difference between an Intel or AMD processor when playing most games if all other hardware components were identical.
Heat isn't a concern for either AMD or Intel processors currently, unless you start playing around with overclocking. Then you need to start looking at upgrading your cooling options over any factory offerings. It's also worth noting, that higher end Intel processors generally don't come with cooling included, while AMD processors do.
If you're into video editing, 3D modelling, content creation, CAD or need to run a specific application, then do some research on the application you use and find some benchmarks for the processor you're looking at buying. For example, here's a roundup for Premiere Pro which shows how a number of processors perform different tasks:
https://www.pugetsystems.com/labs/articles/Premiere-Pro-CC-2019-CPU-Roundup-Intel-vs-AMD-vs-Mac-1320/For the record, I currently use an AMD Ryzen 1700. Prior to this I had both an Intel i5-3570K and an AMD FX-8350, I actually still have the FX-8350.