I'm looking for a program that can monitor multiple AMD GPU temperatures and automatically shut down the computer if the temps reach a certain point. E-mail notification upon this event would be a nice bonus too.
speedfan will do all that.
you'd just punch into the event setting "if (AMDGPU1 temperture) is > sometemp for sometime, then execute shutdown /s /t 0 /c "GPU1 overheating"" and a second one almost identical one with a shorter "sometime" value (so it has a bit of time to send the email before the system shuts down. 10 seconds difference should be enough.) which sends an email instead (remember to put the SMTP server settings into the mail tab).
and of course duplicate both for each GPU.