You can take the volume of the balloon constant and also the pressure of air in the balloon equal to the atmospheric pressure.

Find the expression for ρ(T) knowing that the density of air at 20°C is 1.2041 kg/m

^{3},

(

http://en.wikipedia.org/wiki/Density_of_air)

and apply Archimedes' Principle. The total weight of the balloon and load and the air in it is equal to the volume of the balloon multiplied with the density of the cold air.

ehild