We have Dual Lennox Gas Furnaces (Paralleled) in our basement with a Honeywell TH8000 series Programmable Thermostat on the 1st floor.

We have manually controlled dampers in the supply ducts to allow us to heat only the basement or only the 1st floor or heat both basement and 1st floor.

Can I just add a 2nd thermostat in the basement (none hooked up now, only control is from 1st floor) or do I have to have a zone controller installed just to have a thermostat in the basement?

We don't have Air Conditioning so the control of Heat Pumps is NOT a issue here.

Thanks for any advice I can get in advance...

You will get a low voltage feed back problem through the thermostat.

Would driving a relay with the thermostat or using the built in relay fix the feedback issue?

You could, say, put a motorized damper in the first floor and have a thermostat control it. Have the second thermostat control the basement (colder area) and the furnace. The assumption here being that the basement needs more heat. That's only an idea.

Multiple stats are tricky, but with a gas furnace and no AC, you have it made. Yes, you need to create dry contacts for the heat call and I'd probably use one transformer for the furnace and another for the two stats.

The fan would be an or operation. Either stat could make the fan stay on.

There are some opto relays specifically designed for this purpose. The opto approach is for reliability.

Hopefully you understand the technique. Use a transformer to power both stats and connect each to their own fan relay and heat call relay. Wire those contacts in parallel.

Now use a SEPARATE transformer in the furnace and wire the paralleled contacts to operate the heat call and the fan.