I have a Rheem HVAC unit, model #RRKA-A030JK10E. The air conditioning runs fine, but when I switch to heat it works when it feels like it. Sometimes it will blow strong when I turn it on, and other times the furnace will heat but the blowers won't turn on. I don't understand what is happening. I recently replace the thermostat, could this be the issue? The original thermostat only had four or five slots - basically it had enough for all the wires, but the new one has about 8 slots for the wiring. I put the wires in the same places as in the last thermostat but the unit started acting like I described. Any help would be tremendously appreciated.

Yes I would start with the stat wiring. Can you post the model # on the stat? And a pic of the stat so I can see the wiring?