Help Engine dies when warm

Hi all, I have been reading posts on this site regularly and have found the advice very helpful. I have got a problem with my 1983 GSX250 twin which I am turning into a café racer inspired by similar conversions I saw on this site.
My problem is, it is hard to start cold, its fine after the initial start up. After riding for a few minutes, it loses power and dies. Left to stand for a couple of minutes it will restart, but is very doughy. It seems the problem maybe heat related.
I have noticed that the left hand coil gets quite hot if the ignition is left on, the right hand does not.
I was riding the bike with the side covers of and noticed the rectifier/regulator also got very hot.
I'm not sure if this is related or not, but when the headlights are turned on the idle drops significantly, the bike will stall if the revs are not raised.
Hope someone can help.

 

I have a multimeter I haven't checked for voltage drop yet, its a little hard to start, but I did check the coil windings as one of the coils is getting hot I thought that may have been the fault. Both coils have an ohm reading of 5.5, whereas the repair manual states it should be 3.5 - 4.5. I am not sure of the accuracy of my readings as if the coils are faulty it seems a little odd that they would be exactly the same. I'll try and start it now and let you know about the voltage drop.

Thanks for your input,

 

OK update, I have the seat and tank removed, I fitted a separate gravity feed to the carbies the engine fired straight away. which leads me to believe the starting problem maybe vacuum/petcock related. Would you agree.

Battery pre startup - 12.4 volts,
During engine crank - 9.4 volts.
At 3000rpm - 13.4 volts.
When headlight turned on 14.6 volts.

Neither coil became hot, it was only a short run.

Regulator/rectifier was quite warm.

Does this make any sense.

 

Thanks for the advice. How do I test the RR?