The motor/heater keeps running until the high temp limit switch kicks it off (about 115 F), it doesn't shut off at thermostat setting.

It is an old 93 Hotsprings Hotspot Round, I figure it's a controller relay or thermostat, but can't find a schematic or parts.

Any help appreciated.

TIA,
KC

Bad t-stat or stuck relay. Check to see if if voltage to the element is present when the t-stat is turned up and gone when turned down, have you meter leads one on each electrical terminal for the test.