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« **on:** May 15, 2018, 03:04:04 PM »
In reality there are way too many factors (air currents, humidity, material, geometry/wall thickness) to get an answer here, plus we'd have to take an indefinite integral while I'm on still on my first cup of coffee, but we can go all Fermi approximation on it. Short answer, to get to 2°F above ambient will take a very long time.

Desired heat transfer we do know exactly: 6.6 gal * 3.8 L/gal * 1.1 kg/L * 11°F * 1.8°C/°F * 4.2 kJ/kg°C = 2300 kJ

Newton's law of heat transfer to keep things simple: Q' = hA∆T. Figure a best-guess of 5 W/m^2K and 12"x 13.5" WxD gives hA = 1.6 W/K. Our average ∆T is 7.5°F = 4.2°C so Q' = 6.7 W and 2,300,000 J / 6.7 W = ~95 hours. Assuming constant flux is going to be over by quite a bit due to the long tail, so approximate it as 95*e^-1 = 35 hours.

But as Dave points out you don't need to exponentially decay all the way out to the exact target temperature, so in reality you'll be within a degree or so after maybe 24 hours.