Explain like I'm Five: 2015 Mac Mini 3.0 i7 better or worse than 2011 MBP 16gb 2.4 i7 quad core?

The late 2014 i7 Mac Mini will outperform the 2011 Mac Pro for yur uses. The MacBook has a quad-core processor when the Mini only has a dual-core processor but yur uses really do not use four cores.

If your constantly crashing problem requires the computer to get warn first (that’s often the case for hardware issues) its a good idea to take it into an Apple repair shop ‘pre-warmed’. For example, one of the computers in my wife’s office had that kind of problem but when she took it to the Apple store the genius ran diagnostics and saw nothing. So I made an appointment and arrived early so I could sit out in the mall using it for 20 minutes. It crashed twice while I was waiting for my time slot and I kept using it right up until the moment my name popped up. No problem - it panicked for the genius three times. The repair bill revealed that Apple rebuilt her computer around the hard drive 😁 Seriously, the drive, keyboard, and display were about the only things Apple didn’t replace.

And yes, the mini is going to out perform the MBP but since the new mini cannot be upgraded, get as much RAM has you can afford and I'm not sure that 8GB is going to be future proof. Given a choice between 16GB of RAM and the i7 CPU I'd choose RAM. Also, the default internal HHD is a bottle neck so an SSD is a very good idea.

When you call AppleCare again stress the point that it is heat related. Make sure that it gets into the documentation.