I recently replaced an OLD analog thermostat with a cheap digital thermostat. I thought this would be a simple operation, but it’s turned out to be kind of confusing.
It works, but now the fan doesn’t seem to want to turn off, ever. I have it switched to AUTO / HEAT. Once the appropriate temperature is reached, there’s a slightly different sound to the fan, but the blower continues to run until you manually switch everything off.
Any ideas??? 
Thanks!
I have had a similar issue. My husband wanted to hook up a thermostat that would allow us to just run the fan. So he went out and got a cool new one.
Problem was it’s an older furnace and not wired for a separate control for the fan, as newer furnaces are. So he was trying to hook up a two wire furnace to a more than two wire thermostat. You can do it, but it doesn’t work right. It wouldn’t shut off on it’s own and the controls wouldn’t work the way they were intended. It was very confusing.
In the end, we switched back to a two wire thermostat and solved the problem.
They are not interchangeable and if you try to hook up the newer one, the whole system doesn’t quite work right. If your furnace isn’t wired with a separate fan control wire, a new, more than two wire, thermostat won’t work.
I have to disagree with the previous post. Though they are able to support a multi-wire configuration, they usually also have a 2 wire configuration installation instruction as well.
I have a simple oil burner, hot-water baseboards, and a 2 wire configuration, on a fancy digital thermostat, and had to pay attention to the instructions to get it right. It sends a “more heat” signal (I think by basically shorting the connection internally) when it drops below the trigger value, and sends a “hot enough” (open circuit, I think) when the thermostat detects sufficient heat in the room.
Check the installation instructions. They often have an 800 number.
NOTE: Some systems have special requirements, and may not be compatible with your particular device. There is a replacement available in the same aisle of the hardware store though. That said, you may not have separate control of the two functions (heat & fan) in any case.
Your best bet, if you’re determined to make it work, is to call the manufacturer of your new thermostat, explain your system, and get the correct wiring. I had to do it when I replaced my old builder’s-grade thermostat with a shiny new programmable one, and the specific wiring for my system wasn’t in the manual; they were very helpful. My new thermostat is a Honeywell, and they seem to be the Goliath of thermostat manufacturers, so if your new one’s also a Honeywell, call 'em up.