[torbjorn]

Does it give a proper picture even while the transistor is getting hot?

Check out the waveform at the transistor's base to see that it gets correct base drive and really is saturated during the whole forward scan and instantly turned of when the retrace begins.
If the transistor goes out of saturation towards the end of the scan, you will often get bad horizontal linearity, the right part of the picture will shrink.
A common case for this is a bad decoupling capacitor for the supply to the driver stage. Or, if there is a electrolytic somewhere in the signal path from the drive transistor to the output transistor, then it could also be bad. Also, check for bad solder joints and low-ohm resistors that may have changed value in the drive circuitry.

Another possibility would be some flyback capacitor that has got open circuit, or switching circuitry for changing flyback caps for different horizontal frequencies that does not work as it should.
You could try running the monitor at a different horizontal frequency and see if the transistor gets hot even then.

[macmar]

My AOC monitor Model 7Vlr S774AA, works OK for a few minutes but after a while the horizontal output transistor gets so hot and if allowed to run for a longer time the transistor fails. What could be the cause?