I put in new gas logs with a combination remote control/Thermostat. The fan from the old gas log set is still operational and hook to electrical power. I want the fan connected to the new thermostat so that it will go on and off with the fire.

The thermostat must have an output to drive the gas valve. Right? Check the voltage of the output when the gas valve is on. Get a relay that corresponds to the voltage you measured. Look on the fan and determine the current (presumably at 120 volts) that the fan requires.

Connect the output of the thermostat to the relay's "coil" or primary. Connect the other side of the coil to the same "ground" that the thermostat uses.

Connect a 110-volt source to the relay's contacts or secondary. Connect the other side of the relay's contacts to the fan's input (black) lead. The other lead must go to the neutral. Basically, the relay replaces a switch in the LINE wire. When the thermostat turns the electric gas valve on, the fan should turn on also.

The main problem you will encounter is that the thermostat must be able to provide enough power to drive both the electric gas valve and also the relay's primary. You'll have to determine the current that the relay will draw and make sure that the thermostat can provide that in addition to what it is already drawing. If it cannot, you will burn out the thermostat.