design - Maintaining a constant current with varying loads

I've designed a constant current source using a current mirror, we need an output of about 50mA. The problem is that we build it and heat has become a problem.The transistors and the R_load are both heating up which decreases beta stabilization (our amperage through our load resistor increases constantly). I think that by adding an emitter resistor we should be able to beta stabilize but I'm not sure if I'm doing it right.

Answer

Given the very large head-room you have available from your primary supply, you should be able to just use the 7805 in current regulator mode:

^{simulate this circuit – Schematic created using CircuitLab}

This would accomodate a wider range of load resistors if you could swap the 7805 out for a chip with a lower reference voltage and lower drop-out voltage.