Yes, a worn out engine will run nice and cool. Hope you don't have same issue as me, but mine is definitely a rocket when it's not too rich, but still gets hot. Mine turned 10100 revs yesterday.
I am still messing with carb, seems to be very fine line between too rich and too lean, and several thousand different combinations to try. Next I am going to try different throttle barrel, have 30 installed, and have 40 and 50 to try. As I understand it, 40 will run a little leaner, and 50 leaner still 1/8 to 1/2 throttle. I am going to try W7 needle too, and maybe W9 (don't have yet).
245luigi had link to cool 2 cycle tuning book and I read some of it. One take away I got from book was you want to tune carb to be very close to being too rich. Book encouraged me to keep trying with the carb, might eventually get it just right. I got it pretty close with OEM carb, but didn't have different needles, etc to try. Got real close with 19mm carb with AN nozzle, but then couldn't get the needle I wanted W16. So I switched over the AU nozzle and had to start over. Have learned a ton about Dellorto carbs, ask me anything, I can tell you lol's.
I have also been reading about squish. Next, I am going to check squish in my engine, check combustion chamber cc's, and maybe try adding a cylinder base gasket. I remember a kart engine I used to run Rotax FR125 that had different thichness cylinder base gaskets you could try. Thinner gave more compression, more low to mid torque, thicker more top end power. One thing I remember, engine with thinner base gasket had more compression and was harder to tune carb. I think parallel to what I have now, too much compression, very hard to tune carb. That engine was LC, I think AC harder to tune cause quicker to get too hot, LC can take more abuse.
I never actually worked on that engine, was before I started working on 4 cycle engines. That engine made 28hp and if anything was wrong, it would blow for sure, so I was afraid to work on it. Expensive too, $3000 for engine, $700 to rebuild, etc.
245luigi also linked ParaIndiana Like 50 BBK build, lots of good info, cool vid of him at the drag races with Like 50, looks like ran great. But I will tell you, BBK tuned to run at drags would run too hot cruising 50mph on country road, I am prettty sure of that.
Cheers