Just read an old post by someone that used to pop their feet in a cold bucket of water while at work, but was getting into trouble with H&S for water/PC cables...
So here's my solution to overheating feet and if you make a smaller one, heads too.
Have you tried the ice water bottle (reverse of a hot water bottle)
I use a large empty shop bought water bottle like Volvic as its square so won't roll. I drink the water cos I'm a skinflint.
Then refill with tap water three quarters and shove into the freezer until frozen.
When I need to use it I top it up with a little bit more tap water but not completely full, cap back on and then pop into a pillowcase. Hey presto instant cold feet at work or in bed!