I tried to make a formula that I can use to get an rough estimation of local temperatures.

I have used Boltzmann's formulas of heat radiation from the sun and some formula to calculate the distance to sun and the angle towards sun.

Often the estimatation is less than 5 degrees off. I know there is a lot of factors that can change temperature like albedo, humidity, winds and so on. So just 5 degrees of is very impressive.

Some problems I found when I test temperatures in the middle of the winter never get below freezing. Maybe I just calculated the equilibrium temperature or, when I use boltzmann's formula I took the 4th root to get the temperature, or I did not calculate the temperature radiating of earth...

If you have some ideas to get negative temperature estimates please help, it is appreciated.