The ASIC is probably going to give you a better return on your money than the GPU, and be a bit easier to move around since they tend to be already contained. Since you're posting in altcoins, I'll assume you want an scrypt miner, so if you look at something like a InnoSilicon Terminator Mega 110MH, those things put out some decent heat. They are definitely loud though, so keep that in mind, although you could probably replace the fans with some quiet fans if the ambient temperature is going to be relatively low.
As far as shipping times, you can order those from Innosilicon directly and get it in no time - or look around used and see if there are any deals, although the market for scrypt has been pretty tight lately.
You might also consider the Bitmain Antminer S5, it puts off a decent amount of heat, and with BTC being relatively low these days, you can pick them up pretty cheap.
Either device will mine more than the power they cost to run, unless you are paying some really high rates - and even then, your space heater doesn't pay you anything when it runs.
