Are you saying the fan comes on when you turn up the heat or runs without the heat being on. Do you get cold air at first and then warm air comes out. If that is the case it is because your fan is on a timer rather than a temp switch as they used to have. At one time they used a fan/limit switch with a bimetal that started the fan when the air in the plenum became warm enough so you wouldn't feel cold air. Now they have a circuit board with a timer for the fan. Sometimes the fan starts up before the air is warm enough but as the burner keeps running and the air gets warmer. Sometimes the timer is adjustable.

It runs without the heat being on.

It could be your main limit switch is going bad.
You need to have your furnace looked at.

Since everythibg is most likely electronic have your tech look at it to diagnose the problem. They have the equipment.

Thank you everybody. Removing the thermostat and then setting it to auto seems to have corrected the problem, well see

If your t-stat had a setting for auto and a setting that possibly said on, you want it set to auto. The on setting is for the constant running of the fan. It looks as though you found the problem. Good Luck.