You're going to find a lot of compatriots in the biocube community. Any of these AIO tanks with a lid definitely suffer from high temp swings with the lid closed and lights on. A lot of biocube users end up propping the lid open, cutting new vents or installing a nano-chiller. The cheapest solution that keeps the lid is to retrofit a small fan onto it somewhere and have it blow fresh air into the tank. You can have the fan run on a temp controller or just a timer with the lights. Nano chillers are little less DIY, but are much more expensive in the $150-300 range.
82F is borderline high, but there's tons of tanks that reach that temp without issue too, so I wouldn't stress over it too much if you don't think it's at risk of getting even hotter depending on the time of year.