You can follow Ken's suggestion to find out to true pH of your tap water. If you find the pH is much different from your tank, you can make small water changes. The resulting pH change in your tank is basically the % of water you changed times the total pH difference.
I have a similar situation, except my water starts at 7.6 right out of the tap, but the true pH is closer to 8.2. If I have to change a lot of water, I will put water (2 degrees warmer than my actual tank temperature) in a 5 gallon bucket, and aerate it for 4 hours with a
powerhead. The aeration accelerates bringing the tap water to its true pH. This way, I don't have any problems with the water being too cold for the tank.