If you have now completed fishless cycling, then your water change must be a big one. However s you have no fish in there yet, it doesn't matter too much whether it is warm or cold.
However if you are adding very cold water and you then have to wait more than 12hrs for it to warm up before you can add fish, then there is a chance that your bacteria will start to die off unless you add a bit of ammonia. If you do this, obviously you need to wait for all the ammonia and nitrites to be clear before you add fish.
Personally I never add water taken from the hot water storage (immersion heater as some call it) tank.
Irf.