Insulin + testing kit = cold pack?

Hello folks. Thanks for all your great advice and help previously!

I started on shitty NPH insulin today (gave myself my first shot about an hour ago, hooray...--also, pushing doctor to get me on a more reasonable and normal setup as well as an endo). I'm planning on carrying my testing kit and insulin/syringes together in my pack, which has space for a cold pack.

Should I keep a cold pack in there since I'll be taking this to work with me, or will that screw up my glucose meter?

I'm especially wondering for when the inevitable summer heat arrives.

Thank you for any help!!