You have brought out a very important aspect that the the spectral irradiance F to express in in Wm-2µm-1, the result got from the equation has to be multiplied by 10^-6 . In many text this is missing. I suggest that the equation itself reflect this as given below
I don't understand how does the curve is effected by considering the contribution of all heating parts.
For example,one human emits heat, while a bigger one emits heat as well.