I have a honeywell rth8580wf heating thermostat. I wonder what the output of the "white" terminal is (heating control). Is it only going from 0V to 24V or is it continuous depending on the room temperature?
It's a contact closure. When the thermostat wants heat, it closes a contact between the "Rb" and "W" terminals, which allows current to flow.
Here's a good reference for thermostat wiring in general.