How do trees handle this?
Often the answer is, "not well".
The best way to see what is happening to your tree is to look at the very top first. This will show signs of stress first. The second is to look at the foliage and judge it against healthy trees. The third is to step back and see if there are areas of the tree looking worse than others.
The most difficult part of diagnosing trees is the fact that they don't do anything fast. Heat stress or chemical damage can take weeks to show. So it is crucial that you always look into the history of what the tree has gone through, over the last few months, to make a correct diagnosis.
We will see trees struggle with these extremes in temperatures however, if we feed them and water them properly, most trees can push through one or two extreme stresses.
It's when multiple stresses compound that we see trees die.
UPDATE JUNE 15: That stress we were talking about this early spring is just now showing the damage. People don't understand, or even believe, that a tree will take three months, or, in the case of covering the trunk flare, fifteen years; to show damage from poor tree health care. But that is exactly why their trees often die and they really don't know why.
We are seeing trees die on one side and live on the other. WHY? The tree's vascular system runs fairly vertical. This means that their "arteries" go up and down. So if you damage them on one side at the trunk base, you'll see death on one side of the tree.
In the case of that late freeze, it was severe enough in some trees to actually freeze and damage the cambium layer on one side. The tree had nutrients enough to put on the first round of foliage, but as soon as the heat hit, it couldn't support the leaf tissue with the damaged "arteries" called phloem and xylem in a tree.
The result is symptoms appearing months after the damage occurred. People who specialize in trees see these late results and know that often symptoms can not be fixed. And at the very least, they can not be fixed quickly in a safe way for the tree to react to a chemical or nutrient. If you want healthy trees, you have to be diligent in the care and pay attention to what they are going through.