Welcome to a very addicting hobby!!
I live in Minnesota so I share your concerns. In my experience the basement has a been a blessing! When I got my first cham he was in one of my upstairs rooms and I got home one nice day to find that the room was about 90 degrees so his basking spot was 114!!! I was terrified that I could have killed him. So he moved downstairs...then to the basement due to water issues. If you can keep your temps and light up (I have a huge, almost walk-in egress window in my "cham room" that gets sun all day) I would recommend it. If it is too dark though, I would put up plant grow lights - if the pants can't get enough light to thrive it cant be good for your cham. For humidity in the winter, I learned off the forum to wrap 3 sides of the cage with a shower curtain...works perfectly! And, more importantly, it was cheap!
If the basement isn't an option, just keep windows closed on cool days and keep the cage away from AC vents. As long as your ambient day temps are in the 70's you should be fine but if you are the type that has it snowing inside with the AC on that could be an issue!
I love having my guys in the basement, some ppl don't like it. It works fantastic. I dont have to worry about all the water on my carpet, the temps stay the same, the humidity is GREAT in the summer and fall and better yet, it is no big deal if a cricket or 2 is running lose in the basement!!