I have not had that problem (yet) but I am curious about it causing a draw vs. tripping the breaker.
I ~have~ had a fault to ground due to condensation from a tiny leak in the heating element (or maybe just condensastion under the plastic cover) and I can attest that the breaker will trip at almost nil fault current (like 35milliamps). I would replace the thermostat first (cheap) and the heating element second (maybe $80 U.S). The hard part about those Quick brand boilers is that the heating element almost requires a 55mm socket to break them loose. Luckily, a Toyota wheel bearing socket is exactly right.
AnchorExpress.com has the heating elements and Thermostats although their delivery time is long. I got my new thermostat from eBay, actually but the heating element (plus a spare) is on the way.
Funny to me is that the original Stainless boiler gave zero trouble until it just died, but the new and improved all plastic one seems more prone to faults.
Ah, it's the sailing life for me :)
-Waiting for Arthur to pass-