Suitable replacement for 2SC2001 transistor? BC337 doesn't seem suitable
What could cause transistor to overheat? Well, it's whether excessive base current, or excessive product of Ic x Vce.
This is your circuit:


Base current is not a problem, it is limited by R128 to 4.5mA. So, transistor could overheat by high Vce or Ic.
Say hFE=200. Then maximum Ic=900mA. But it will be lower, say it is 500mA. Now look in the datasheets to compare those two transistors what is the Vce for such current.
This is from 2SC2001 datasheet:


Vce=0.3V
So power dissipation would be 150mW, well within specification.  

This is from BC337 datasheet:


It is off the chart, it is a bad sign for this situation. Vce would be much higher than 1.0V, say it is somewhere around 1.5V.
So power dissipation would be 750mW, which is above maximum allowed power dissipation.  

I do not say your circuit is drawing 500mA, peaks could be higher or lower. But you can see that in some situations there are differences between BC337 and 2SC2001.  

Another relevant difference could be in hFE. It depends on your batch. There are huge differences:
2SC2001 (hFE from 90 to 400)


BC337 (hFE from 100 to 630)


So you could compare BC337 and 2SC2001 with very different hFE (you maybe compare BC337 with very low hFE, and 2SC2001 with higher hFE).  

And the difference can be even bigger in hFE because hFE changes with Ic: