Yes, this is theoretically possible and I presume you mean that the temp switch would be set so that when it was hot, it would switch on, and a light would be wired to it. There is already a temp sensor that drives the thermostat but I believe it is on the input side. Your idea would give me the secondary light that tells me that both the UM506 is on, and the thermostat is closed. This might be neat, but doesn't achieve my primary objective of only indicating the UM506, not the thermostat. You see, if I know the UM506 is off, then I know the heater can't come on, no matter what the thermostat tells it to do. (the UM506 and thermostat are wired in series. Both have to be closed for the heater to be on.)
Sorry I have to go into a bit of detail to describe some seemingly irrelevant background..only technos will want to read:
I have a hot tub with a high and low speed pump switch. The pump speed must be on high whenever the heater cycles on. This is because the heater is a 250K BTU one that is also used for the pool so it can create steam and pressure if the water is not moving at a certain speed. The amount of water that pumps through the hot tub at low speed is simply not enough to release the amount of hot water created when the heater is on. So, right now I have an airswitch to turn my pump from high to low. I have an X10 remote wallswitch near the hot tub to turn my UM506 (and therefore the heater) on and off. The heater thermostat is enabled when the UM506 is in the on position, so of course the heater comes on only as it needs to, to keep the water hot. After I use the hot tub, I turn the pump to low, and turn the UM506 off at the same time. Due to the vagaries of X10, I'm worried that I'll turn the pump on low, but that the Heater won't actually be turned off. Then the next time the thermostat cycles on, the heater will damage itself. So, to be extra cautious, I either listen for the barely discernible click that the UM506 makes, or I end up having to walk a few paces, barefeet in the snow, down to the pool shed, to see that the UM506 actually turned off. (which totally wastes the need for the remote X10 switch in the first place) A little LED light would be so much better!
So the end result of all that detail? I don't really need to know if the heater is actually on at this very moment, I need to know if the UM506 is on, even if the thermostat is open, and the heater off.
I sure wish the UM506 had its own LED light. Then I would simply splice in some extension wires and move the light to a location on the outside of the shed that I could see.