At what temp do deciduous tress decide to wake up? I understand that species are different and that there even differences within species.
In general, they 'wake up' when temperatures rise above 40F/5C or so.
However, many temperate species and all alpine ones have a bud chill requirement that must be satisfied first. For example, consider the case of a tree that requires 1,008 hours of accumulated chilling time. Were it in an environment where the temperatures stayed below 40F/5C continuously, buds would break as soon as the temperature rises above 40F/5C. Nothing happens if at some time before that the trees were taken out of cold storage, say, and exposed to temperatures above 40F/5C. On the other hand if the trees stay cold for 6 weeks and then experiences a 'thaw' for a few weeks before a last cold snap happens, your trees 'didin't pay attention to the calendar' - they broke bud, leafed out and got severely frostbitten; possibly killed.
Suppose one lives in a climate where the winter temperature drops below 40F/5C only overnight so that only 8 hours of chilling occurs each day, on average. It will then take three times as many calendar days, 18 weeks or 3.5 months, to accumulate the chilling hours and only after those 3.5 months will buds will break.
Then, of course, one may be in a climate that doesn't produce the required chilling time. As the temperatures warm and daylight hours lengthen, some buds may break, but growth will be weak and the tree will loose vigor and ultimately dies within a few similar seasons.
Chilling hours are well known only for a few important lumbering species such as Douglas fir that requires at least 1750 chilling hours. I have several and live in a Douglas fir forest. I have many Japanese maples; they appear to have a chilling time requirement short of 1,000 hours. Indeed this varies by cultivar. A.p. "Orange Dream" is always the first to leaf out in my collection; a.p. "Higasayama" is later. I have many, some deciduous and some evergreen that all appear to have different vernalization requirements before they bloom. I also have 'early blooming' azaleas that don't require much, if any, vernalization and they are blooming now, right on schedule. Since these are evergreens and not very frost hardy, I believe that they sense the passage of the winter solstice like tropical trees do. That would mean they really are calendar readers, but I'm guessing now.