It’s obviously a thermal issue of some kind, as GuanoLad says, but the symptoms sound a bit off for a bad solder joint. I would expect that to be worst when the set was just turned on, then stabilize once it was warm (assuming “warm” is its operational mode, as suggested by the problem only showing up when it’s cold). Instead, it’s going out after it’s been warmed up for a while.
It reminds me of a problem with a model of Goldstar TVs back in the early 90s that worked fine in summer, but almost invariably went dead at the first cold snap. Like many CRT sets, they relied on a thermistor to shut off the degaussing coil. When you turn a set on, the thermistor is cool and low-resistance, allowing the coil to be energized and demagnetize the screen. The heavy current warms up the thermistor, cutting off the current to the coil. The problem was that the thermistor started off cooler in winter, and took a fraction of a second longer to warm up…which was just a bit too much for the slightly under-rated fuse, so it opened, killing power to the set.
Bearing in mind that I’ve not been an active technician in many years, so I may be speculating off into the tall weeds:
This problem could be similar. Most sets suppress video while the degaussing coil is active, IIRC, so you don’t see rainbows and swirls and think the TV is possessed. So, it’s starting normally (dark during the degauss, then displaying video when the degauss finishes), then the thermistor cools off enough to drop it into degauss mode again, and it suppresses the video until the thermistor heats back up–which could be a while if the circuit is just over the suppression threshold, and the coil isn’t fully energized. A thermistor that has gone out of tolerance could conceivably do that.
I’m normally in favor of people being able to fix their own stuff, but I would recommend against messing with this one. If the problem is in the degaussing circuit, it’s prime ground for a nasty jolt–that runs directly off the AC line. It’s past time for a new TV, anyway. (The CRT itself is far, far past its prime, even if nothing else were wrong).
Be prepared to make at least a couple of trips to the store. The first one is a scouting foray, where you note down the model numbers of the sets that look best to you. Then go home and look up the models, compare stats and reviews, read up on some of the less obvious features, and shop around online. (You don’t want to try to look at the comparison charts on a little phone screen with some salesdroid smarming at you.) I’d recommend checking out Samsung or LG* flatscreens; they’ve got some very good sets for pretty reasonable prices.
*Despite the Goldstar story above. They’ve gotten rather better over the years.
