How do I tell if my tree is stressed by hot/dry weather (or just stressed)

Hot and dry weather can induce stress into trees (and plants).

This is due to either the heat and the lack of moisture (or both).

To start with the leaves can look limp/wilted and/or lose their lustre.

If the situation is not rectified (watering, moving potted plants into shade (and watering), the next phase is the tree thinking, it makes more sense to loose some leaves that keep loosing moisture through them. Some of the leaves (sometimes all), turn their autumn tints and then fall.

If any of the above occur your tree is stressed.  You need to water (taking care you do not over water), frequently, ideally morning and evening, until the weather has passed.  Then continue watering over summer at a reduced rate.

The loss of leaves is a reaction to the conditions, typically the tree keeps the branch alive*, new leaves may be produced this year or next.  If the stress is extreme the tree will dieback in then canopy to a size that it's root system can support**.

Another reaction that the tree could produce to being stressed is basal or epicormic growth. These are new young branches that appear from the base, trunk or bases of branches. These grow fast and straight as they are diverting energy that the tree does not think is worth sending to the canopy.  For  this reason they should never see a Sunday, prune leaving a small collar (to make the surface area smaller and easier to repair).

* You can check if a branch is still alive  by scratching the bark to see if a small green layer just below the bark is present (the cambium). If it is the branch is still alive. If it is not the branch has died back to this point.

** If this occurs, let the tree dieback (whilst watering etc), it will withdraw reserves in its branches as it dies. If you proactively prune back before the branches die back the tree will lose this energy.