I'm an EE, but I haven't studied Burton's wiring diagram, so I don't really know how Zero wires things up (Burton's diagram is for the S, anyhow). But I'll add a few thoughts.
At least on the S, Zero does use a DC-DC convertor, made by Sevcon, which also makes the motor controller. Clearly all the stuff you're describing would be powered by the DC-DC convertor, but I'd be very surprised if the dash isn't, as well. That would lead me to believe the DC-DC convertor is not causing the problem.
What you're describing sounds to me more like a flaky connection somewhere. Fuses don't show a lot of pathological behavior, but connectors sure do. I can't tell you how many times I've seen intermittent behavior and managed to track it down to a connector pin not fully seated, usually making contact but not always. The temperature dependence you're seeing seems to point the same way -- something expands a bit and makes contact, or shrinks a bit and loses contact.
I think first thing I'd do is go through and inspect all the connectors leading to the controls that aren't working, including disconnecting them and seeing if any of the pins don't look fully seated. Work the connector a few times to make sure it isn't hanging up on anything, and the connector shells are fully mating. I'd also throw some dielectric grease in there while you're at it.
If that doesn't work...well, since Burton hasn't made a wiring diagram for the SFX, and I doubt anybody else has one either, I'd just take it to the dealer.