Hot air rises. Close the door leading to the basement. Install ceiling fans in the bedrooms to help keep you cool at night. Contrary to popular thought, air moves best in an upward motion, so when you have three floors and allow air to move between them, the warmer air will always rise up.

Thank you for your reply. I'm not sure I understand - in the summer, the second floor is too warm. What are you suggesting that will help balance out the warmth in the second floor with the too cold in the basement?

If you have a single HVAC system serving multiple levels in a home, the challenge is to direct the right amount of air on each level for its respective heating/cooling load. Loads are rarely the same on each level. Installing an automated zone control system is one way to improve comfort. Even if your system isn't zoned, balancing dampers are typically installed which should enable you to direct more or less flow to each level--if not each room. Here's a link to a video that explains it clearly:

https://www.google.com/search?q=youtub+video+getting+rid+of+hot+and+cold+spots&ei=sZegZI-GCdjokPIP9KuWkAs&ved=0ahUKEwjPoouVt-7_AhVYNEQIHfSVBbIQ4dUDCBA&uact=5&oq=youtub+video+getting+rid+of+hot+and+cold+spots&gs_lcp=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&sclient=gws-wiz-serp#fpstate=ive&vld=cid:ef322b44,vid:8dJbLTEXyfg

I’ve never heard of someone insisting that a 3 level house have the exact same temperature on every floor. It’s normal to have variations. You can install specialized equipment, or you can close off the basement and put fans in the upstairs bedrooms to keep everyone comfortable. You can also program your thermostat for a daytime temp when you are on the main floor, and a nighttime temp for when you are upstairs sleeping.

I have a two-story home. I expect comfortable conditions on both levels year 'round. That's where proper design comes in. Each floor in my home is served by its own system. I also have balancing dampers which enable me to balance the individual room air flows. I do that on my 1st floor seasonally for comfort in the master suite.

Installing multiple temperature sensors is an alternative to zoning, but, unlike zoning, it will deliver heating or air conditioning air flow to spaces which may not be calling for them and may produce uncomfortable conditions in those spaces. It will also run up the monthly utility bill.