Why does my air conditioner come on when I turn on my heater on my 98 Ford Taurus?

Check the blend air door. It sounds like it is stuck.

I agree with what you said, but my problem is that the heater blows "cold" air when the heater is properly turned on. Even when the temperature control is turned to the warmest setting.

There is a door which - when actuated by the temperature control **** on the head unit - switches or blends the air flow. For heat, more air flow will come through the heater core, and for cooling, more air flow will come through the A/C evaporator core. There is an electrical device called the "blend door actuator" which actually positions this door according to where you have the heat/cool **** set. The blend door actuator could be at fault (probably most likely), or the blend door could be obstructed from movement, or the head unit's heat/cool control switch (or associated wiring) could be at fault.

I've attached a couple of illustrations that I hope will help.

**** = k. Nob