First off..... thank you so much for that link Kurt!
Some great info. there.
I purchased these nest boxes from either HD or Lowe's - I forget which. Made of 3/4" thick cedar. Yes, as Robin pointed out, there is a good area of ventilation in the front there under the overhang. There is also ventilation in the rear which you can't see. There is some as well in the bottom but I know heat rises not sinks so I'm not counting that ventilation for much value.
Can't get any hose there & not sure that would do much anyway. I think it would be a very temporary benefit.
Right now I'm not going to do anything. Mama is there sitting on eggs. I don't want her to desert the nest. Many, many broods have been successfully raised in that box over the last 3 years.
Elaine, I do have a gloriosa lily starting to climb that lattice. However, that probably won't make any difference this year as I suspect this is the last clutch for the year. Next year though, the lily will be established & by this time of year will be shading the box.
This winter I will paint it white and drill some more ventilation holes in the top sides.