Aye Dan,
Welcome to the forum, others maybe along to chip in their pennies worth; here's mine for a start.
I have a 1986 SRX600 'Sally', don't ask

and starting was a bit hit and miss, cold or hot. I suspect that the hot starting problem is due to the fuel in the carbs evaporating due to the heat after a good run. Or else the coil insulation may not be liking the heat and breaking down, but I think that this is unlikely. Sally sometimes 'dies' after a good long run, with fuel starvation, inspite of the tank breather being clear, the cure is to switch to 'PRIME' on the fuel tap and then revert to the vacuum 'ON' position. If your vacuum hose is old and perished, its replacement, maybe the easy fix.

Also, try priming the cylinder with one or two gentle kicks, with the ignition 'OFF', this helps ensure any loss to evaporation is avoided. But beware, you may get a cracker of a backfire, when you turn the ignition back 'ON' and give the motor a good swing!

I would suggest a check of the air cleaner and fit a new one, if necessary. I'll leave the choice of OEM or equivilent to you. Maybe fit a K&N, as I did 12 years ago, although the current price is horrendous, they are fit and 'forget' (almost), and being washable last the life of the bike.
Check your spark plug and renew if at all in doubt, I use an NGK Iridium plug (DPR8EIX-9 Iridium), again they are no cheap, but fitting one made Sally easier to start and smooth running.
Check that your choke plunger is not siezed in its bore and that the whole mechanism is free to move, including the cable. They often come out looking like a good Thai red curry sauce if the water has got in and started to corrode things. refurbishment parts kits are obtainable from NRP (
NRP_link) or Wemoto (
Wemoto_link).
Check that the fuel filters in the bottom of the petrol tank, carburettor and any supplementary ones fitted in the fuel lines are clean.
Check your valve clearances, they may be "tight" when the motor is hot, adjust if necessary.
And check that coil, just in case.
The other thing to check is the generator as this supplies power to the ignition, regardless of the condition of the battery and if the shellac is startinmg to break up on the coil windings with heat, this maybe another problem. But, as I have said before, I would check the fuel side of things first. Sally is now up to 120,000Kms and seems ......
If you need a workshop manual, I can supply a reasonable pdf copy FOC. Private Message me with your email address, via the forum and I'll send one across. The PM link is on the left side of the message window, below my avatar.
I hope this helps.
My regards, Bill