Just to keep the ball rolling, I have my doubts about this.
Several sites give specs on the temperature coefficient of such variable capacitors and the numbers run at around 100 parts/million/[sup]o[/sup]C. For a 400 picofarad (pF) capacitor this amounts to 0.8 pF for a rise of 20 C. If the receiver is tuned when it is first tuned on it will drift about 2 kHz when tuned to a station at 1.5 mHz if the temperature goes up by 20 C. However, once the temperature stabilizes I think it will not drift around since the variable capacitors are quite stable in their mechanical properties.
My speculation is that the drift is from an electronic tuning element such as a varactor that is erratic in its temperature characteristic.
You two are the devil! So, how can I figure out which type my radio uses without opening it up? Because, mind you, I very likely will open the thing up if there isn’t any way to figure this out without doing so, and I may very well end up breaking the thing, but now I’m intrigued and have to know 
The more I think about it, I’m less sold on the ambient-temperature-is-causing-fluctuations idea, because the temperature in my apartment doesn’t change THAT much, I’m not using it outside, and I don’t leave it running all day while I’m not home. Also, I think what I was seeing as a trend in when/where the signal “drifts” to wasn’t really a trend so much as a feeling from non-controlled studies… so I’m less sold on the explanation I’d latched onto earlier
If it helps, the radio is part of an approximately 10- or 15-year-old “boombox” on which the CD player no longer works, which I only use for listening to radio in the morning and at night. I’m fairly certain the signal is stronger in the morning, but I’m less certain about any pattern in the “drift” (having to re-tune to find the peak of the signal).