Hope someone can help:
Anywhere below being set at 70 degrees, our furnace blows cold air once it reaches the desired temp. It blows, and blows, and it feels almost as cool as AC! I have to go physically to the actual furnace to switch the switch off and then on and it stops. The "fan" switch on the thermostat thingee on the wall is not turned on, but in auto mode. (which is the only option other than on).

If I set the thermostat ABOVE 70, it will warm us beautifully, and shut the furnace off when desired temp is reached without kicking the blower on. Which feels like it is the way things should go... The problem is, the 70 degree setting is too warm for us to sleep but I need some heat, and NOT cool air, blowing at night for my baby to keep warm enough in her nursery.

Anyone? Thanks!

Is this a heatpump? It could be only the aux heat strips are working and not the outdoor unit. Thus the fan will run all the time.

I don't understand what switch you are going to the furnace and turning off.

You are right in settnng the fan switch at the thermostat to the "Auto" position.

If your thermostat is set for 70 degrees and it reaches that temp does the furnace fire turn off? And after a few minutes does the fan turn off? If it does not it could be a problem with the fan switch on the furnace. If you can understand how to do it raise the off temp at the fan and limit switch to about 110 degrees and see if this makes any difference.

If you can not figure out how to change it send a picture of the fan switch and maybe someone can help you.

More info about the system (brand/model # etc.) would be very useful here.