I'm relatively inexperienced, so perhaps this isn't quite right, but I would still think that with a heater it would be concerning. My house is normally high 60s, low 70s and I have a 30 gallon community tank and a 3 gallon betta tank. The temperature easily stays around 78 in both. My family went on a trip for a few days last month and when we got back the house was in the 50s. Both tank temperatures dropped from high 70s to, well, the 30 gallon temperature sticker on the side didn't even register a temperature because it was so low, and my betta tank was like 68 or 70 (I have a regular thermometer for that one). I even lost a platy a couple days later because he couldn't handle the change. Amazingly, my betta, sick with severe fin rot survived it and is still hanging in there!
My dad has a tank in the basement too. He is always struggling to get the temperature into the high 70s. Either we have crappy heaters, or the heaters just can't handle such drastic outside temperatures. If you have a pond outside, it can get much colder than our basement!