The First thing I would look at is the variable tuning capacitor.
My first Idea is that at the lower frequency, the capacitor plates have been bent somehow. As the set warms up the difference is enough to make the shaft expand. This could cause the plates at the bottom end of the scale to touch and short the signal to ground. Some sets have a screw adjustment to center the plates.
Another thing to look at is the padders. Some one may have adjusted those and set the padder to cause a short. They should have a mica insulator in between the top metal tab and the bottom one. Look for a small screw on each section. There should be two. One for the oscillator section, and another for the antenna section. If you adjust these slightly you may see an improvement, especially if some one has monkeyed with them.
If the stations are on the correct frequency marks on the dial dont touch the oscillator padder. It could be that there is a problem with the the first tube in the antenna section of changing interelectrode capacitances during heating up. Also a capacitor or a resistor may open or short during warmup. Take a plastic pen or small wooden skewer And tap on different different components after the set warms up. If you do that be sure to be on the lower frequency so you can pinpoint the defective part. Some resistors drift in value during warmup so that could be a clue to start measure resistance values. They should be no more than 20% off value.
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