Mac Pro 3.1 with strange behavior

Hello everyone,

I am having a problem with my Mac Pro 3.0 (A1186) and would like some help identifying the cause. I have seen several questions and answers about Mac Pros on this site, but I would like to submit my specific issue. A little over a year ago, I had the following problems; random shutdown and restart, Kernel Panic window, fans that run at high speed when starting or waking up. I then took the computer apart to dust off the components and put it back together. I also replaced the clock battery. When the computer started up, everything was fine and there were no problems for several months. In the last two months, during very hot weeks, the same problems gradually started again. Now, the following situation always occurs on startup;

- I start the Mac and everything works normally.

- After about 5 minutes of use, it will turn off and restart.

- It works fine for about 2 minutes then turns off and tries to restart.

- At this time it fails to restart but sometimes it goes to the blue screen and then turns off.

- From there, the computer stays on, the screen is black, the fans are spinning normally, and it no longer attempts to start.

- Also, I can observe the fan on the top of the video card (ATI Radeon HD5770 1GB) which rotates by increasing its speed gradually then decreasing it and this alternately.

- Finally, I shut down the computer by holding down the power button.

I suspect video card or internal temperature management could be the cause, but I'm not sure. I have left the computer unplugged for at least two days after removing the clock battery, but the same situation occurs on startup. I also removed the startup disk that I installed in an external enclosure to plug it into an iMac 24 ”and it works fine which leads me to believe that this disk is not the cause of the problem. Any information that might help me get this computer back up and running would be greatly appreciated as we use it for work with software that is not compatible with a version newer than Mac OS 10.6.