Personally, I'd pull out the heater, as if the water is 70, the heater is probably about 75, and he's just sitting near it instead of getting out to warm up. Odds are your house is about 70 degrees anyway so the heater will rarely turn on. Mine is set to where it only comes on when I do water changes and the water is pretty cold.
I keep my basking area in the high 80's to 90. Even at that heat, they stretch their necks out to get that extra inch closer to the heat. I figure these animals are cold blooded and use the difference in temps to regulate their body heat. By giving a wider difference, it helps them to regulate their heat. Granted, you don't want to freeze or burn them, but a wide range works well for me.
I have 3 turtles that are all about 4" and havn't ever had any illness or shell problems. They love basking and love swimming. They're very active.