I agree with heating the whole environment. A heating pad would have to be used under half the cage only (in case it gets too hot) and that would have no change to the air in the cage. A ceramic heat emitter or a space heater (both with temperature controls) would be best in that situation. That way you know the temperature will remain the same all the time in the entire cage. If you use the ceramic heat emitter (which is basically a heat lamp that doesn't put out light and is made for reptiles), you don't need the heating pad also.
As for the wheel, a comfort wheel or flying saucer are the best choices out of commercial wheels--other brands can damage nails and cause injuries. Any of these wheels need to be 12" or bigger in diameter (so comfort wheels you need the XL version); anything smaller than that is too small for an adult hedgehog.
Bucket wheels are the better option, and many people sell them on personal websites. They typically run about $30.
The best option of all is the Cake Walk Supreme wheel, which is 100% custom made for hedgehogs. They are very easy to clean and run $40--but they are also well-made and will last you forever. The Cake Walk wheels are the ones most worth your money.
I just wanted to mention, since you're in the basement: be SURE to keep the cage elevated off the floor. The floor is the coldest place in a room, especially in the basement. The room temperature could be 75*, but the floor could be 68*. Because of this, you need to keep the cage elevated on some kind of stand--and be sure the cage is entirely escape proof with a lid (that has ventilation holes) so you don't have a fall on your hands.