RRC 3.5 EFI starting problems when warm, battery power low.

Hi guys,
My RRC starts with relative ease when cold, but if I take her for drive long enough to get engine to max temperature, after I turn her off she wont start again for about 10 minutes.
When I turn the key the response is very low battery juice. My batteries have been checked and are fine. If I wait 10 mins she will start again no problem.
Also when she is warm and wont start,, if I attach jump leads from a spare battery I keep in the boot she starts first time.
Alternator is working.
Very frustrating.
Also when I turn the key over when warm and low juice in battery,, if I keep turning her over smoke comes from the wire coming out of the starter motor solenoid.
This wire is after market and goes to the bulk head where it meets a main battery feed?????
It is live,,,,
Please help any one.

When warm does the engine turn over on the one battery, if not its most likely corrosion in the system,
Get the resistance meter and start checking every cable and joint, remake joints where you can.

2 issues perhaps, the other being the coil, or ign amp perhaps, but more likely the coil

Y I would of gone coil n amp but the feller goes on about voltage and battery, TBf It's also an option if it's turning over well

I renewed the cable feeding the solenoid, seems to have fixed it. Thanks

1-0 to Pete