Constant Current Source BJT
You have the variation in the large signal model with Vbe (and beta) as the transistor heats, but there is more to it than that. 

I think you should use the hybrid-pi model for the transistor. With a "stiff" voltage source on the base, the output resistance of your current sink is ro, which is related to the Early Voltage Va that you will find in a transistor SPICE model.