Let's start with the basics ...
What does "It the shows that it has no battery as it will not start up until it cools down for a while" mean? Do you mean that nothing works until it cools down - to me - no battery means no lights, no horn, no radio, no crank - and no crank is different to no start.
If it goes completely dead - no lights no radio - start AT THE BATTERY - the problem will be either the battery itself, the battery leads (check the leads from the battery negative to the chassis and from the positive to the main fuse panel under the hood), and also the main fuse in that panel.
The main fuse panel is where the positive feed splits to go to ignition switched loads (the ones that work when the ignition is on) and non switch loads (the ones that work when the ignition is off), so if everything goes dead, the problem is either in that panel or between the panel and the battery.
Edit.
One last thing - I had a somewhat similar problem with my 98 2.0 Grand Vitara - whilst driving everything would die for a second or so and then come back to life - at first I though it was just the engine, but as day turned to night, and I switched the lights on, that was when I discovered that even the lights were dieing for that brief moment.
I checked the cables and the fuse panel - found nothing loose - and even the the battery showed no sign of dieing - it cranked the car EVERY time I tried - I put a new one in - and the problem went away.