Once you have a light going in a tent it'll be a lot warmer in there. Just going to get cold air entering when you open the flaps to work on your plants. How big is this basement? Mine is more of a large underground crawl space that's 10x30 and about 7.5' tall. My grow room was built by the previous owner as a cold storage room and had shelves all around. It's about 7x9x6.5'h. Two walls are just OSB board on cement and two are insulated 2x4 stud walls with a heavy wooden door I installed a dead bolt on. smooth, painted cement floor that drains to a sump in case of spills.
When I first went to view the place that room sold me. lol I had a bunch of plants in my grow room in the garage at my place in town. Got the place for 50G and sold my dump in town for 32G. Tiny lot in town with a POS '74 12x65' mobile home and 20 x 20 insulated/heated garage. This place, 7.5 acres, 1990 16x80' mobile with 6" walls with 17x34x10'h heated shop, my 15x12' mancave with same size mudroom and a 20x35' carport all attached as one unit. The old guy started asking 175G then kept lowering the price until my wife saw it in the paper and we scooped it up for 50. Stuck in the middle of nowhere but can just do whatever I want and there's no one to complain. Shoot my guns, crank my stereo and grow lots of stinky pot to my heart's content. Two nice whitetail deer in the front yard yesterday. Dog near freaked out. lol
If you have space upstairs then you might be better off up there during the cooler months then you could always move the tent downstairs in the summer if the tent gets too warm. Bit of a PITA but with the wife helping should be easy enough. How about venting tho? Can you be cutting a vent hole to outside? For a 3x3 tent a 4" vent should be big enough. Wasn't for my room but I'll run 3 x 4 HPS or a 1000W sometimes so a lot more heat to deal with. There was 4" already but I cut a 6" hole in the stub wall to vent out under my shop. Has a metal flap vent on the outside. Like a dryer vent but bigger.
Environment is important for good growing especially in the flowering stage. Not such a big deal in veg I find. My exhaust fan has a home made almost RH/Temp and speed control on it so it only runs when needed. Thermostat on the heater so temps are steady day or night. Good circulation is a must so an oscillating fan is best. You might want to rig a shelf or something to hold a fan up over the canopy to move air around. Not sure how small you can get in an oscillating fan. I have a 12" going 24/7 to keep the air mixed up well. If you could find an 8" that would be enough.
I have enough lights and gear to do 4X the space I have now but plans to expand and I'm one of those guys who likes backups for his backups.