I am fairly new to Linux. I have done enough to figure out how to dual boot windows 7 and Mint. I love checking out different distros just to see if there is that one that I'm going to like better.

I am using an old Toshiba Satellite A215-S4747.

I have tried several of the very small distros as I think I would like a very small and fast distro since I mainly use it for internet and watching videos. I have tried several of the puppy distros and derivatives, porteus, DSL, and several others. I can't remember them all.

Most of them I have tried to run from a live USB to see if I would like them. I have liked the puppy distros and really like Porteus. However, every one of the very small distros have one thing in common. Within 5 to 10 minutes of booting up my computer will shut down. I don't even mean go through the shut down procedure. I mean literally on one second and the off the next.

This doesn't happen with any of the larger distros either on USB or installed to hard drive. I have run Mint, Ubuntu, Korora and several others and not had this problem once. The only thing that makes any sense to me, and that doesn't mean much, is that there is some sort of issue with my ram as it us my understanding these smaller distros attempt to run straight from ram. Any thoughts or suggestions? I would love to be able to give these smaller distros a try, but it isn't worth my time if they won't run more than 10 minutes without shutting my computer down.

Most likely those small distros (especially DSL, using a 2.4 kernel that is not suitable at all for somewhat modern PCs) lack in proper power-management and overheat your system, leading to the shut down. In any way, seeing the specs of that machine, there is no need for low-spec distros, just go with one of the general purpose distros, especially when you don't want to fiddle with things that are that essential as power management.

1 members found this post helpful.

I can do that. Really do enjoy Mint. Things seem to be a little slow, but I have been checking out some of the slightly smaller distros.

There are many fully featured, but more lightweight distros, look for example at Mint MATE, Xubuntu or Lubuntu, Bodhi or antiX.
Many of the general purpose distributions also have the option to only install a basic system from which to build up your OS like you would like to have it, but this needs of course more work and slightly more knowledge (at least how package management on that distro works).

I actually would like to to give Bodhi a try. It looks nice. I have run it from usb a couple of times and it simply does not acknowledge that I even have wifi. I have seen the ubuntu derivatives and will check them out. Not familiar with antix but will go look. Thanks for your help.

It definitely sounds like overheating

If you liked Mint, try the Xfce version.

AntiX is basically an installation disk for Debian which gives you light-weight software and the old but nice Ice window manager. Although it was intended for old computers, it's sufficiently popular for new ones to justify a 64-bit version.