The A/C and heat seem to work OK. Just when I have the temp control all the way cold (without A/C), a little bit of heat still comes out the vents, several degrees warmer than the outside air. Is it normal or should I be looking for a problem?

 

check to see if the air mix motor is moving when you change the temps.

You'll have to climb under the dash on the driver side, look up from the gas pedal. You should see the air mix motor.

With the key on, have a friend (or if your limber yourself) move the heat/cool lever on the logicon. The airmix motor should move the same. Check to see it is not binding or stopping before full travel.

If it is not moving at all, you have either a bad logicon (needing resoldering or replacement) or a bad airmix motor (which generally takes the Logicon with it when it goes.

*edit
Or, I have seen once where the Logicon plug right above the airmix motor was loose, you might check that as well.
**end edit

A new airmix motor can be found at http://www.mazdaformance.com/rx7.htm which has the best price on them that I have found.