R.K.
If you can sew at all make a little case with velcro straps to hold it in place. It should look like a small pillow case with straps attached to one side of the open end. Make it just big enough for the ice packs you already have to slide in.
Good luck my feet were hot too. It could be swelling that's causing the feeling of being hot. Make sure you are drinking enough and put your feet up as often as possible.
Congrats on the tiny person.