I have a Remington Model 7 in 7-08. The first shot out is dead on, the following shots always go up and to the right stringing about 1" apart with 3 shot groups. I have been careful not to heat the barrel up. Driving me nuts, any thoughts, Please.

Sounds like an immediate candidate for glass bedding. Vertical stringing = symptom.

Take a piece of business card or match book cover. Fold it over 2 or 3 times. Place it between the forearm and the barrel and tighten it down. It may solve your problem without having to bed it.

Ignore those businescard tricks, it's like lengthening your blanket by cutting slice from the top and sewing it back to the bottom.

This is quite good article: http://www.6mmbr.com/pillarbedding.html

I just use blu-tack instead of clay and I center those pillars by wrapping some tape around action screws. I also glue pillars before bedding, because this way it's easier to adjust action to correct place. After that you remove some wood around the pillars to gain some space for bedding compound. Remember to use 2-3 layers of masking tape on sides, under and in front of the recoil lug to avoid mechanical locks, but only if one of the action screws doesn't screw into the lug. If action screw has hole in the recoil lug, don't use tape under it. I have used ProBed 2000 bedding kit, it has everything else, but pillars, has worked this far.