I guess I could see if an insulated lunch box or something along those lines would help cut down on the heat. I don't know about adding any kind of ice pack though because it could cause moisture as the day goes on.
Put the phone inside a zip lock bag inside an insulated lunch box with just enough of those refrigerated blue plastic ice cubes so that the temperature inside the lunch box rises up to near typical use temperature (neither cold or hot) at the end of your work day. Then when you take it out you won't have to worry about condensation. Your Li-Ion battery will appreciate it.