MFD Works Only When Hot

Hi All,
I'm having an odd problem with my Multi-Function Display (MFD), or rather the problem with it is stranger than I used to think. It stopped working about a year ago -- at first just going blank intermittently during drives, then failing to start up at all. I'm used to driving without it -- the audio system and climate controls all still work fine when controlled from the steering wheel buttons.

The strange thing is that I recently parked the car in the sun and started it mid-afternoon when the cabin was hot (maybe 85 or 90 F), and the MFD started right up and was fully functional that whole drive. I replicated the temperature part of this several times -- starting the car at night when the cabin is cool, the MFD does not power on. But it reliably does when the cabin is uncomfortably hot from being in sun.

I was convinced this must be a failing 12V battery that was able to supply the necessary power for the MFD only when it was "helped" by being at a high temperature. And the 12V was in fact old, and producing sub-par no-load voltages, so I figured I may as well replace it before it stranded me. I did so, and the new battery is performing well (12.8 V when measured without the car on), may have even improved fuel economy a bit as mentioned in a few other threads on here.

TL;DR: What could be causing the MFD to start only when the *cabin* temp is high, other than the 12 V battery? Is the traction battery involved in starting it up somehow (the car still gets good gas mileage and I don't have any other signs of a failing main battery)?

Thanks for any hunches!