Strange problem with Heating

[BPLuvr]

I don't actually know and am straight up guessing here but I would hope an overload would trip a breaker or fuse. Herpstats are very sensitive to 'dirty' power (need pure seine wave energy) if they are used with anything else they often don't work at all, or look like they are but do not regulate.

Very true a full overload would trip the breaker (if it's not faulty). Pushing high enough amps, close to but not high enough to trip the breaker could cause a voltage drop. With your explanation of the Herpstat needing the clean voltage that may very well be what is happening.