How to remove a Carrier / Bryant Infinity thermostat control from the wall

Here's the installation manual for that thermostat: http://www.emersonclimate.com/Documents/White-Rodgers/instruction_sheets/0037-1558.pdf

You're right about L1 and L2, and about it not mattering which is which inside the thermostat housing. It is a single throw switch so its terminals are interchangeable.

The yellow triangle labeled "2" in the diagram is any device you want to turn off when the temperature gets too high. The installation manual uses an oil burner as an example of such a device. In your case you'd leave that switch unwired, unless you want to rig up a solenoid valve to douse your wood fire. :)

There is a set of connections in the air handler that usually includes the "C" terminal, and it should be labelled (though it may be hard to read depending on the location of the control board and/or wiring/etc in the way).

One way to tell for sure is that while the furnace is not running, using a multi-meter you can measure between the "C" and "R" (or Rh or Rc terminals) and you should see 24VAC. R (or Rh and Rc) will already be going to the thermostat.

As an example, on your furnace, from the manual:

The colors may match, but don't count on it. The sure-fire way is to check using a multi-meter as I said above.