The transistor I originally used myself could drive 800mA but it was only ever intended to drive a former DVD red up to about 300mA so this tranny could handle that without a heatsink. The more current you pull the more likely you are to need a heatsink. Your red will prob be ok, but depending on the size of green you are using (assuming you will drive green through this as well) you may have to heatsink as a green pump diode will pull lots more current than a red diode for lower output. For example a 100mW green may pull as much as an amp whereas a red (DVD Diode) will output 200mW from 300mA. The other limit will be the circuit design - see below
The limit with pulling higher currents is the 1ohm resistor and the power supply voltage. As I said the driver was designed for maybe 300mA or so so the 1ohm is fine but as the current goes up this 1 ohm is too restrictive and at higher currenst drops too much voltage that there isnt enough to go round - so ohms law dictates that the current will go to a point then stop increasing.
As you go up un current you need a smaller resistor - drivers for 2W pump diodes in green and blue lasers will have something like a 0.33ohm resistor instead. As far as blue diodes go they will need 4V across them to work (red diodes drop 2v - give or take) so the power supply will need to be a higher volage for these to work at all.
I would use the circuit as you see it for red and lower the 1ohm to 0.33 or 0.2 ohms (may need to experiment) for the green and blue with a higher supply voltage (maybe around 9V)
Rob