That is hooked up to the furnace that works in the regular way. The second thermostat would be downstairs but would control only the furnace fan so that when the temp drops downstairs the first thing that happens is that only the furnace fan comes on to mix the air in the house (cold downstairs air, hot upstairs air)to give an even temprature. If that solves the problem i.e.. The downstairs temp will rise when mixed with upstairs air and the #2 thermostat downstairs will shut the fan off because the temprature has risen a small amount. The #1 thermostat will only activate the furnace if mixing the air via the fan only drops the #1 thermostat temprature low enough to warant it.
If this can be done it seems to me to be a good way to solve the hot upstairs cold downstairs problem that lots of people have.