Don't make assumptions.
Test!
Open it up, run it under full load for 10 minutes, then measure temperatures. Is the transistor actually putting out that much heat? How about the output diode, or capacitors, or the transformer?
Typically, power is evenly distributed through all these components, plus snubbers and other minutiae. You can reduce loss in any one component, but mind the sausage effect: example, a bigger transistor has less Rds(on), but more switching loss and more drive power. More drive power means more auxiliary power (controller) dissipation. More switching loss means more snubber loss.
The transformer will be your elephant in the room. You can't really change it, due to footprint and form factor; and even if you find another the same size, makes you think the new one will have any lower loss? (You can purchase new cores of lower-loss materials, if you're willing to go that route -- but if you're limited to salvaged parts, who knows?) You can use more turns (less flux density --> less core loss), but you have to use thinner wire (or fewer interleaved layers) to fit it on the same bobbin --> more copper loss. Again, the losses (core and copper) are normally distributed evenly, so there isn't much to save here.
If you put it in a larger enclosure to accommodate all these changes (beefed up parts, maybe even a chopped up PCB to make everything fit), you still have the problem that, after all this screwing around, EMI is probably worse. (There are very real cases were switching loss is traded for EMI, so if you're strictly optimizing for efficiency, you will end up with EMI being much, much worse!) If nothing else, you're changing the components and layout, which is likely to change EMI by -- who knows how much. Safest is to put it inside a metal enclosure, with line filters on both ends, so the noise stays inside.
Tim