In honor of Thanksgiving: take a look at Niall MacKay’s paper Of bombs and boats and mice and men: a random tour through some scaling laws.
I mention this because one of the scaling laws there is the time it takes to roast a turkey – you can work out from dimensional analysis that roasting time is proportional to the two-thirds power of mass. Specifically, the thermal diffusivity κ of meat (or any other substance) – that’s the constant in the heat equation – has dimensions of length squared over time. Since the only relevant parameter is the length of the turkey l, roasting time must be proportional to l2/κ. But assuming a spherical turkey, length is proportional to the cube root of mass, giving the two-thirds law.
Happy Thanksgiving! And for my readers abroad, happy Thursday.
God plays dice 
I would have said that you have to heat a colume by head transfer through a surface. More surface area is faster, more volume is slower. Surface is proportional to length squared, volume to lenght cubed. Hence 2/3 power law.