How do I calculate the required average world temperature for specifically-sized polar ice caps?

I know the average world temperature is 59掳 F. How do I calculate what the average world temperature would need to be for the ice caps to generally/on average be at, say, 32掳 North/South, or any other specific latitude?|||In my opinion, I don't think this would be very difficult to determine since the energy is not evenly distributed , the earth circulation is not uniform or constant, and temperature sensors for estimating the earth surface temperatures are mot evenly collected in a grids like system or a even density fashion.