Runs hot & drains battery during sleep--not a hardware problem

I have a 2017 Macbook Pro running High Sierra 10.13.4.

A few months after I bought it, it began to have some graphics glitches. Then it began to run very hot (like sizzling!) while unplugged and asleep. If I left it unplugged/asleep/lid closed for an extended period, it would drain the battery within a few hours.

I sent it back to Apple under warranty and they spent 3 days running diagnostics, then declared that it was not a hardware problem, but must be caused by software I had loaded. I was also advised not to migrate my old Mac contents onto the new laptop and not to use a Time Machine backup, but to reload individual programs by hand.

I did this, gradually reloading my software a little at a time, hoping to catch the culprit. A month later it's happening again, but removing the software has not helped to reverse the problem. So, maybe some change I made to settings...or maybe malware...or something? is causing the computer to run while asleep, to the point of draining the battery. I need to fix this and Apple will not help because they say it's not a hardware issue.

My question is, how do I diagnose what the Mac is trying to do while it's asleep? Activity Monitor doesn't help because as soon as I open the lid, the computer stops doing whatever it was doing. (Notably, it cools down a lot when I wake it from sleep.)

What should I be checking for? What are likely culprits?

(Note: please don't tell me to zap the PRAM or reload the operating system or any of those obvious first-step troubleshooting things...this has been done and redone many times and doesn't work). I need to know WHERE TO LOOK to find software or setting problems that are making the computer check something fruitlessly during sleep.