When heated up my Samsung SM 710v goes blank - Samsung SyncMaster 710VT TFT LCD Monitor

Could be a lot of things. Fortunately, there is a relatively easy way to figure one of these problems out, but it involves taking the unit apart enough to access the electronic components, which I have never done with a Samsung, so you will have to get some other help to figure that out. Once you can get to the electronics, you turn the set on and wait until it goes blank...then you spray "cool spray" on the various components, one at a time, until the set comes back on. Voila, you found the heat sensitive part, so now you have to replace it. That will be another fun experience, but if you can get that part replaced, chances are you set will work fine.
Another scenario is more complicated, since some part may be drawing too much current, and a shut-down circuit is being triggered. A schematic and knowledge of electronics is needed in this case. Get an estimate before you get it repaired by a shop. Sometimes you're better off buying a new one, unless you can fix it yourself. You could try a low noise fan, blowing on the back of the tv, as an afterthought...might get you by for awhile.