Heating elements do not have an in rush current, like motors. And any fan motor that would be on a space heater wouldnt have an in rush that's worrysome. I'm using a 1500watt heater on a herpstat hp with no issues. So either your heater is messed up and pulling more than it should, but not tripping the breaker which would have to be a pretty specific short or the herpstat is messed up.

Could verify by using another high wattage item like a hair dryer and seeing if you can replicate the problem.