A room becomes warmer when the person arriving is greeted before their lateness is discussed.

Whoever walks in late already knows. They have spent the journey composing an explanation, and the first thing said to them decides whether they spend the next hour recovering or simply join in. Leading with the delay, even lightly, makes their arrival about a failure. Leading with the welcome makes it about them being there, which was the point of inviting them.

Say their name and hand them a drink before anything else. Let the explanation happen or not happen on its own. If something practical needs covering, tell them quietly once they have sat down.