I would accept that it's quite practical to have a 65 KW battery, evidently so did NASA that's what they said the one aboard took care of all the power needs of the LEM for 3 days.
OK, so let's start to look at the numbers for the power needs. To do the precise calculations would require an equivalent design effort to that used by NASA, which obviously I can't do. Instead, I will look at some simple calculations to establish some ballpark figures. If any of these is problematic, it can be calculated more precisely. You mentioned temperature maintenance, so I'll start there.
The crew cabin of the lunar module has a volume of 6.7 cubic meters. Assuming a cubic shape (for simplification), this means a surface area of 21 square meters.
I don't know what type of thermal insulation was used, but it would be at least as good as ordinary expanded polyurethane (which is routinely used in building applications). This insulator has a thermal resistivity of around 1.4 meters squared Kelvin per watt-inch. Let's solve for Watts, using an assumed insulation thickness of 2 inches, and an inside-outside temperature difference of 200K.
This gives 21m^2 * 200 K / 2 inches / 1.4, which equals 1500 watts. Over 72 hours, this would require 108 kW-hours. OK, the first rough calculation needs a bit too much power. But wait! We have a highly-reflective layer on the outside. This alone has a thermal resistivity of around 10, or 12.8 when we add it to the two-inch expanded polyurethane layer.
Now we need a power consumption of 21 * 200 / 12.8 which is 328 watts, or 23 kW-hours, which is well within the capacity of our batteries. Of course those batteries must do lots of other things too, but I hope this "back-of-the-envelope" calculation has shown that it's entirely plausible.
At this point I should mention some other things. The crew module was deliberately placed on the side of the LM that would be in the shade during the mission, which would have reduced the power requirement somewhat. Oh, and the LM cooling was actually provided by ice sublimation rather than by electrical power, so it imposed no load on the batteries anyway.
Are you prepared to accept that the need to cool the LM doesn't in itself make the mission implausible? If so, we can investigate some other aspect of the mission.