One problem with soft and hand puppets in warm weather is sweating into the puppet.
A way I have found to protect the inside of the puppet is to take a white tube (athletic)
sock and cut two holes in the toe; one for the fingers and one for the thumb. The
bridge between the holes keeps the sock from sliding up the arm. Between shows toss
the sock into the laundry.
If sweating is serious you may want to do the same thing with the plastic bags newspapers
are delivered in. While you can use it instead of the sock, I recommend putting over
the sock. Plastic against the skin get sticky and uncomfortable fast, not to mention
the sweat running out of the bag.
For all cloth puppets I recommend cleaning them in "Dryel" (or another brand) bags.
These are home dry-cleaning bags. A special cloth is placed in the bag with the puppet
and put in the dryer for around 30 minutes. I'm not sure this would work with puppets
that have latex parts.