here is the proof that tar paper doesnt work the way people think.

the average temperature in the box is when the heat losses equal the heat gains. The heat loss or gain is proportional to the temp difference multiplied by the time by the proportion of surface area being heated or cooled.

lets make things simple the fraction of the day that is daylight and hot sunshine is t and therefore fraction night is (1-t). The fraction of the box exposed to sun is B. The differnce between the box and night temp is N and the difference between box and sun lit surface is S

B.t/(1-t) = N/S. (this equation is an approximation to the full solution)

so if we have a 6hours of day light and the sun only reaches one side in six of a cube, then the difference between the box temp and the sunlit surface is 18 times the temp difference between the box temp and night time temperatures.

example:

ambient = zero C

sun facing surfacetemp = 54C (that a temp too hot to keep your hand on for more than few seconds)

Average boxtemp 3C

lets go the other way:

ambient -20C

required box box temp -10c

then sunlit surface temp needs to be +160C