A C370 with a defective protection circuit generally fails in a specific way. The amp will work fine when cold, but after being on for several minutes, the protection circuit will activate. Power cycling will not help, unless the amp is allowed to cool fully before the next attempt.
Well if you found me by the google because precisely this happened to you, you’re in luck. I just repaired mine for the wonderful sum of 63 cents.
To perform this fix you need to be somewhat comfortable with a soldering iron, and be willing to take your amp apart. If you aren’t very good with an iron, you’ll want to read through some how-to pages elsewhere until you’re comfortable with replacing through-hole capacitors on a printed circuit board.
My C370 ripped apart on my workbench
The protection circuit
**edit: According to Stu in the comments below, some amps have 63V caps, so I guess slightly larger caps might fit. Either way I wouldn’t recommend replacing your capacitors with new ones of a lower value than stock**
For those who are interested, here is the schematic for the protection circuit:
NAD C370 Protection Circuit Schematic
Diode on the back of the board