It was to the better of my understanding that the heat shrink goes onto the bars to provide insulation (keeps the heat from transferring directly to the bars).
I am not sure about the tape provided, it may be to hold both ends of the adhesive heat-pad down and prevent it from coming undone when putting the grips on. Needless to say, the grips should not melt, even on the highest setting. I've had mine on all winter without issue.
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