I had two Macintosh Pluses that did this.

One I sold, but I still have one.

Mine would sit there on a white screen then trip, after about a minute. I then sold one and kept the one that looked better. However when I got it back out about a year later, it turned on with garbled image, If I thumped the side it would boot up. However it would then trip after about 5 minutes.

In my case I attribute it to the Flyback transformer slowly falling off the analogue board due to bad solder. However I am scared senseless of opening ANYTHING with a CRT in it!