Replaced the thermostat and furance won't put out any heat. Pilot light is on and fan will run in the "on" position Any ideas?

Did it (furnace) work before you replaced the tstat? You may not have wires connected right. You say the fan is working so this tells me there is power. You might jumper the red and white wires ,this bypasses the tstat and the furnace should fire up and work if the furnace is OK, and it tells you the prob. Is in the tstat or the wiring of the tstat wires