Heat Problem

My 89 Dodge Shadow has a heating problem. We have done replaced the Thermostat, radiatior fan motor, coolent, cooling modual, belts. It happens if you do not turn on the A/C on. But when the A/C is not on it gets up to 4 ticks before hot then the radiator fan will turn on. We have done replaced the belts and tighting them up. This is a 2.5L Fuel Injected turbo engine 4cly. It also has a problem when staring. When the engine gets hot and when I turn off the engine and start it back up a puff of black smoke comes out of the muffler. I know it is not carbon on the piston because I run It everyday. PLEASE TELL ME WHATS WRONG?!

Cooling fans usually run on a dual system. The high speed fan operation is controlled by the coolant temperature switch and controls the temperature at which the cooling fans come on. An AC request controls the low speed fan circuit. Your description sounds like the coolant temperature switch is going bad and coming on at much to hot a temperature.