The primary difference between drilling FDM printed plastic and wood is that the plastic part is not solid the entire way through, and that plastic will melt or burn at much lower temperatures than wood.
If you know before printing that you're going to want to drill the part or potentially need to, then you'll want to modify the design of the part such that there will be sufficient internal reinforcement and material in the location of the drill site. The way I've done this in the past is put a through hole through the the entire part and slightly undersize the hole. Then I also increase the number of shells on the part so that the threads will have some extra material to bite into.
If you know you're going to need a hole in the part but not sure where then I'd suggest using the highest level of infill possible on the print so that your part will be as close as possible to being solid plastic. Or if there are a few areas you think might need to be drilled you can build your own internal structure but that can take a lot of time.
If you didn't know your part was going to need to be drilled AND you printed with minimal infill then be very careful about drilling and only use minimal pressure to cut through the top layer to avoid crushing the part. Then once the part is drilled all the way through consider filling the part with an epoxy to reinforce the hole location (if necessary).
Best case scenario though is knowing where and how big you need the hole to be before print. Of course though specs change on the daily.
As for the heat generated from the drilling process I haven't had much trouble with dissipating it. My 'method' for drilling a printed part (technically reaming) is that after I align my hole with my drill press, I then tap the drill-bit cutting only a millimeter at a time, then retract, wait a few seconds then repeat until all the way through. A little time consuming but my reasoning is to minimize burning and overheating of the hole due to the cutting friction.
In all honesty I think my drilling approach is overkill. But, every time I've needed to do it has been due to an error in modelling. I didn't have the time to reprint and was under a time crunch. My post processing step therefore did not have the option to fail so I was extra careful. Whether it was overkill or not it definitely worked, and it's always better to be a little more cautious than late.