Back again with results. I mounted two old, 80 mm, 12 V, DC fans on the radiator and they work like a charm (third photo). I took the bridge rectifier too on the radiator and now it stays cool even without thermal paste. Basically everything that's on the radiator (three 2N3055's, one 2N3054 and the bridge rectifier) reaches a maximum temperature of 32 degrees Celsius. On the first photo you can see 28.3 degrees Celsius, the temp of one power transistor. Things change a bit on the second photo, because I lowered the voltage to 10 V and the temp of the same power transistor rose to 36.3 degrees Celsius; I say it's still reasonable.
OK, now what's up with the rest of the components? The values above were the result of a quite long (~1 h) stress test: I used a 24 V/100 W Philips incandescent light bulb as load. The maximum power drawn was around 100 W (23 V/ 4.3 A). The transformer got quite warm (reached 50 degrees Celsius at a given moment). The 20 W resistor went up to 51-52 degrees Celsius. The hottest of all was the 5 W resistor on the LCD: 70 degrees Celsius.
Plus here's an interesting situation: as you see on the second photo, I brought down the voltage to 10 V, current went down to around 2.64 A and a few moments later I heard a high pitched noise. It was coming from the small 100 uF/ 63 V capacitor. I touched it and it burned my finger. I don't have an explanation to this behavior which is not present at higher output voltages.
It seems to me that all major components get hot in certain situations. I might need to drill holes on both sides of the case and mount one more fan on the top cover to blows cool air inside.
Finally, I would like to point out one more thing! This variable power supply has a big disadvantage: it can't stabilize the voltage.
As I reduce the current with the help of the current pot, the voltage decreases too. Quite sad that I just noticed that. I don't know if there's a reasonable explanation to that, but in my head the voltage should stay still as I lower the current. Or I'm missing something?
As always, your thoughts are welcome! Cheers!