Test the T-stat and htr relay. Htr relay coil is 110v dc, voltage across t-stat may be either 110v a.c or d.c, dpending on how it's wired (look for a rectifier). Voltage across the T-stsat may open and close actual htr relay (if so, it's dc), converely, if it energizes the rectifier (which then would energize the heater relay) it is a/c.
If it's d.c, a new T-stat (part #75087 from Hot Spring Spas) will have instruction on converting the T-stat to a/c accross the points. You'll get much longer use out of it in this fashion.
A little history... the t-stat was originally wired a/c, but the engineers thought it would last longer dc. so they inlcuded wiring instruction to inlude the addition of a diode and some minor re-wiring.... turns out the d/c caused more damage to the T-stat points than a/c, so they are now including a kit to put it back the way it was.... the point of the story: If it's been changed and converted, change it back. If it's the priginal T-stat, just replace it without changing anything....
Why did you buy an element if you weren't sure the old one was bad?
