Gas and Oil Home Heating Furnaces - Trane Gas Furnace Won't Shut Off

Okay, I'm entry level, so here's my problem...
The furnace runs constantly, the blower for sure, and I'm assuming the heat is running too, because it was 83 degrees in my house when I woke up. I can set the Tstat all the way down to 50 degrees and the furnace still runs, even if I turn the Tstat off and turn the blower to auto it still runs.
The Tstat is a Taystat 340/350, and I noticed the indicator for heat/AC no longer appears on the screen, and thought the Tstat may be bad, as I've heard this model is junk. I've also read possibly the limit relay that tells the furnace when heat is required may be the problem.
The way I've handled this so far is to kill the main power after the house warms up and then flip it back on when it gets cold. When I turn the power back on, the furnace comes on immediately.
Any help would be appreciated, I dont want to buy a new stat if it isn't the likely cause, but I really don't know much about HVAC. Thanks in advance!

Dont short it or turn the power off and pull R off the tstat. Turn power back on. If the furnace dont come on we know its the tstat????? ;)

okay, turn the Tstat off and pull R, then turn tstat on, or turn furnace off, pull R, then turn furnace on? and thank you for the quick response.

also, am i on the right track here, either the Tstat is telling the furnace that it's cold and needs heat, or whatever accepts the signal from the Tstat thinks that the Tstat is telling it that it needs heat, stuck realy, bad communication board, or something of that sort?

Most likely is a bad stat or pinched wire causing constant call for heat to the furnace. Follow Ed's instructions.

thanks guys! I think it was the relay, not 100% sure because it stared working normally on its' own last night. I had the power off all day and when I restarted it it worked fine, so I think the realy stuck closed, we'll see. Thanks for the help!