New thermostat for hydronic heating, no wiring labels, 3 wires
You say, "the fan would come on with a manual switch".  Do you mean the "fan" switch on the old thermostat?   Or a line voltage switch elsewhere, like on the fan itself? 

Normal T-stat wiring is 24v with one wire as the "hot", another as the common and the third as "switched", IE controlled by the t-stat set point, turning on or  off the heating equipment.   The advantage is, assuming the new t-stat is a modern programmable type, that under normal operation, the t-stat is powered by the 24v transformer and the batteries are used to maintain the clock and settings during a power outage.  Other wise the t-stat runs off the batteries all the time and you'll have to replace them about once a year or so.   If you are trying to control both the fan unit and the heat source (heat pump? Boiler?) separately, you don't have enough wires unless you run the new t-stat on batteries all the time.   Was the old t-stat strictly mechanical?