Re: 4,192 KWh
well batteries are coming close to 100% efficient (we'll call it 99% for the sake of argument) in terms of losses for charging and discharging, so really it is a very low amount. You lose more in the power electronics (inverter/rectifier etc) connecting it to whatever it's connected to (grid/solar panel) which are around 97% efficient.
Couple the cooling to a heat pump, which transfers 4 units of heat for every 1 of electricity (i.e. sometimes marketed at 400% efficient, but doesn't break the laws of physics as you're transferring heat energy from one place to another) and you actually have a very small power demand to keep the thing cool. maybe 4% of peak charge/discharge capacity, which might be a few kW, so we're talking about the same energy (10W heatpump for 40W heat removal) to light an energy saving lightbulb to remove said heat per 1kW power input/output.
And you'd accept a lot more than that anyway, as proper heat management prolongs the life of lithium chemistry batteries. The reason your phone battery lasts 3 years is because it follows you around through the heat and cold. Keep it in a temperature controlled room and you'd get 10 years out of it.
So in short, the extra heat generated by a battery charging a discharging, even and big one, is probably about as significant as the heat you get from a desktop PC.