What kind of meter are you using to measure? Read this white paper on Phantom Voltage and see if it applies.
https://www.nema.org/Technical/Documents/Bull_88_reaffirmed_12_15_11.pdf
Does it have a low impedance setting?Fluke multimeter
Does it have a low impedance setting?
Is supply conductors running in same conduit as other still energized conductors or within bundle of still energized non metallic sheathed cables? That will increase capacitive coupling effects if answer is yes.
I see you mentioned it goes away when disconnecting transformer lead which may lead to possible interconnection with other 24 volt controlled units and getting a backfeed 24x120 (or whatever your supply voltage is) through the transformer? If this 24 volt control is isolated and not possible to be interconnected with another source maybe there is capacitive coupling on the 24 volt circuit?
Unless it is a multi-pole switching Tstat, I'd say is a good chance you have backfeed from interconnection of the 24 volt control circuits. That chance is even higher if the 24 volt secondary is grounded in both units as the EGC will connect both grounded secondary conductors together, even though one unit is "off" it can still get 24 volt from the other unit.The heater is run with another unit of the same Tstat.