I'm trying to understand how wild shape interacts with the temp hit points provided by eldritch cannon's protector feature.

Here is the scenario:
1. Artificer puts out eldritch cannon and gives temp hit points to the party
2. Druid wild shapes
3. Druid takes damage
4. Artifcer re-applies temp hit points in the next round

My question is more or less order of operations with hit points within wildshape.  Does the druid wild shape carry those hit points and we remove that damage first?  In this scenario every time the artificer applies temp hit points it buffs the wild shape form and allows for the  druid to stay in wild shape much longer.

Or do we exhaust the wild shape hit points first and apply the temp hit points to the druid's "natural" form?

Since the artificer is giving the druid temp points every round I am confused as to when the druid gets out of wild form with these hit points.

Essentially I need to know if temp hit points provided by the artificer allows for the druid to stay in wild shape longer.