Why not put a resistor (for heating) and a bit of foam insulation on the crystal?

This is way more direct than spacebar heating.

You could also add a transistor attached to the resistor and a GPIO and use the clock drift as a proxy for temperature. PID is probably enough but since you have a 24 hour cycle you could calculate a baseline heating schedule.

This is a technique that's been used for crystal oscillators for almost a century by now. I have some 1950s crystal ovens that are a little metal box that fits over the crystal (quite a large crystal, about the size of two or three SD cards stacked) and heats up to around 75°C. The crystals were supposed to be specially cut to have close to zero temperature coefficient around that temperature so the slight up and down drift caused by the thermostat wouldn't affect it.

I have test equipment made as recently as the early 2000s that uses a crystal oscillator in an oven as a frequency standard. It takes a good five minutes to fully stabilise.

I did this at one point, putting the pi directly on some packing foam. It for sure dampened the ambient effects but really I just need to stick the whole Pi in a temperature controlled chamber.