Thermostat Wire Receiving Power when Disconnected from Furnance

Thanks in advance to anyone that can offer me some advice on this....its driving me crazy. I have a two zone heating system (upstairs and downstairs) each with an individual digital thermostat with 2 AAA batteries, 2 wire only, no AC connected. Over the past few days my upstairs heat will not shut off. The following have been my diagnose steps: * I have set the Tstat to the off position, yet the heat continues to run. * I raised the heat until I heard the Tstat click on, waited a moment, then lowered the heat substantially until I heard it click again (presume off)