Fish obtain their internal temperature from the water so it's always a good idea not to have dramatic changes. This is why we float fish bags to slowly equilabrate temperature. Water used for a water change can be a few degrees either way from the tank temperature. Remember that even when doing a 50% water change, the water temperature added is being offset some by the tank water temperature.
Some feel that slightly cooler water is like rain in nature and stimulates fish to spawn. I tend to think it would take a large very cold rain to alter the temperature of large bodies of water. The excitement of fish is more likely due to fresh, clean water.
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Now although we tend to manage tank temperatures on average 76°F to 78°F, most tropical fish would be fine at room temperature of around 72°F so lets say 5°F lower temp. during a partial water change is likely to be fine.
But lets explore why you have trouble getting around an appropriate source water temperature...
For some tanks I use a 45g trash can filled with cold well water that slowly comes up to room temperature. In the winter, in the cool basement, I use a 300w heater to heat this water prior to partial water changes.
For other tanks I may use sink water with a hose adapter. I have found the appropriate hot/cold setting and indexed the faucet using a sharpie pen. I monitor the tank temperature during the refill and adjust as/if necessary.
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So the temperature needs not be exact, but within a few degrees and the closer the better so as not to shock the fish.
I hope this helps some.
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