So you cannot get cool/cold water from the tap? Perhaps cool some plain tap water in the refrigerator and mix it...? I assume there is some issue behind this...so I'll move forward.
A change in temperature of the water in the aquarium is usually not problematic provided it is slow (i.e., natural, due to the room temperature adjusting slowly) either up or down, and provided it is not too great of a change. Fresh water as in a partial water change should be close to the temperature of the tank water. It can vary up or down but not by much, or it can cause a shock that could be stressful at best and fatal at worst.
Changing smaller amounts of water more frequently can help get around a significant temperature change when you have no control over the fresh water temperature. However, there is no point in adding water that is much warmer and then cooling it somewhat quickly in the tank. This too may be too much too rapidly.
Byron.