When I was an EMT, my issue kit was a soft bag. Biggest problem I had was the cold packs getting smashed and activated, then when I wanted one, it was all used up. I worked in a really hot climate, dark blue bag in the back seat of a B&W Mustang or Camero, or the black painted trunk of a Crown Vic, and I never noted a problem other than the inadvertant smashing...
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OBG