'63 GE B&W clarity troubles

[Thyratron]

I've got a '63 GE 17" B&W (can't remember the model right now, but I can get it if need be), which has some trouble with picture clarity. Upon turning it on and within about the first 20-30 minutes, the picture is quite clear, considering the type of set. However, after the set has had a chance to really heat up, the picture begins to degrade and become very grainy, sometimes to the point that it will begin to roll vertically out of the range of control of the vertical hold knob. At times, it will become unwatchable and will need to be shut down. Anyone have any ideas as to what I might look for as a problem?