Cooling fan still on?

Hi, the electric fan will not stop running once it has been switched on at the temperature that it should come on at. Once the temperature gets down to the point at which it should swith off, it remains running until I turn the ignition off and then back on. Have any ideas as to what might be causing the problem.

I have replaced the relay not that long ago, that doesnt mean that it couldnt be bad, I will replace it again. Let me ask you this, is the coil in the relay for the fan switched through ground or though power. I ask because I noticed that my headlights will not turn off unless the key is in the on position. If I turn the key off first and then turn off the lights through the switch in the car, then the lights will remain on untill the key is turned to the on position at which point they will turn off provided the headlight switch is in the off position. That leads me to belive the coil is switched through ground. Are the lights and the fan on the same circut somewhere? Could I have a bad ground? Or maybe I just got lucky and I have two bad relays? Thanks for your help.

1995 jeep cherokee, rad fan stays on, heater switch only works on high