My 68030 runs hot, probably around 125 or more degrees.
THIS IS NOT NORMAL!!! The typical CPU heat is around the 50°C range, even in very heavy software load. Check the +5V line. Undervoltages are a common cause to malfunction, too.
The +5V rail must be in the 4.85 to 5.25V range and steady (no variation).
Other than that you must replace the Amiga PSU or it will die in a very near future. Also replace electrolytic capacitors in the accelerator board and motherboard.
Dry capacitors will decrease the necessary capacitance required to filter electrical noise and make semiconductor chips to overheat, too.