i agree fully with green, the reason your engine has a thermostat is so that the motor will reach a higher operating temp. "controlled" higher temps let the motor run on less fuel, produce less emissions and cause less internal wear. by controlled i mean not reaching the point of diminishing returns (overheating) and beyond the threshold of the cooling system.
my guess is whoever did your swap (you?) wired up the fan incorrectly or the new motor's coolant temp sensor is shorted. but that's the lesser of your two problems. if your motor had a thermostat in it, the fan running all the time would not prevent the car from getting to temperature, again, like green stated. remove the thermostat housing and put a thermostat in there. then if you desire to do so, check the resistance across the two pins of the coolant sensor (the one in the thermostat housing you just removed) with the motor cold. then again once it's up to temperature. if the reading is the same, or anything like 0.1ohm, the sensor is shorted, replace with a known good sensor.