Most heaters have a thermostat that turns on the heater when the water temp drops below the set temperature and turns it off again when it reaches that temperature. The room temperature shouldn't affect that operation.
The only issue might be that in a colder room the temperature difference between your tank and the room is greater and your heater might not be powerful to raise the temperature by that greater degree.
This is a useful guide on how much wattage a heater needs to raise the temperature by 5, 10 and 15f for various size tanks. Based on this you need a 100w heater.