Maybe probe clocks if you can. That could be due to marginal timing and (parallel) bits being read out of order, for example.
Supplies are a good bet, as timings and performance in general depend upon them. Electrolytic capacitor ESR varies with temperature, particularly towards end-of-life. That's one supply checked, but I don't know how many that thing uses, and I would guess there are more to go. You might also need to check local supplies, in case some sections or chips are supplied by RC filters for example, and there may also be toasted or marginal tantalums, stuff like that.
IC timing constraints also vary with temperature. Presumably something else is responsible for the timing failure -- it would be very strange for any given chip to fail by developing poor timing -- but perhaps something at the start of the timing chain, or bus mastering, or etc., is doing it.
Tim