How to replace the thermal sticker?

Specifically, the little rectangular black sticker that connects the fan housing to the heatsink. When I was upgrading my fan (from the Delta fan to the Huaying fan), the thermal sticker lost its stickiness, and now the ends and the top edge aren't holding very well. The Deck also seems to be running hotter than it should be when playing 3D titles, which forces the Huaying fan to spin up enough to be audible.

I've read that the purpose of the sticker is just to route airflow and not to transfer heat between the heatsink and the fan housing, which sounds right but I don't actually know this for sure. I have electrical tape at home, but IIRC electrical tape adhesive can fail above 80C, and this would be going right on a heat pipe. It wouldn't be a huge financial hardship to just order a roll of Kapton tape and use that, but I also don't know for sure whether that would work.

Any tips?