if the thermostat has a "fan" switch, off/auto/on, then the fan should be wired separately to the thermostat, and there should be a separate control relay circuit.
if the thermostat does not have such a switch, the fan should be wired to the same control circuit as fires the burner, so it only runs when the burner runs. Sounds like the fan might be wired straight to the power line, so it's always on. There's nothing inherently wrong with connecting it that way, as long as you don't mind the fan running all the time. You'll actually be able to extract a slightly larger amount of heat out of whatever fuel you're burning, during the "cool-down" part of the cycle. Of course, this is at the expense of increased power consumption, and noise.
Unfortunately, if it's been "cobbled" together, all bets are off. It could be completely F'ed up. Your best bet is to scour the internet for a wiring/connection diagram for your heater, and redo EVERYTHING. If it's cobbled together, and doesn't work properly, someone obviously had no clue what they were doing, and the quality of connections is probably poor, and could be a dangerous situation.