Temperature changes when you top off or do water changes will depend on the volumes involved (tank and amount of water added) and the temperature difference between them.
I would never add outdoor-cold rain water to any tank, too cold even if i only needed to add a little bit.
I would add room temperature water to a tank, up to about 10% if it was a tropical tank, full water change is OK if the tank was already room temperature.
Best way to deal with this is to have the new water as close as possible to the existing water, within 5 degrees for a 50% water change. That way there is only about 2 degrees or so of temperature change either way. (The substrate holds the temperature too, so the math is right: 5 degrees difference in the new water creates no more than 2 degrees net difference with a 50% water change as long as it is not a bare bottom tank).
I have also used an aquarium heater to maintain the temperature in the garbage can, but I prefer to pay for gas to heat the water than electricity. Cheaper.