While I have nothing against modding the bumper you might also want to replace your thermostat. They are pretty cheap and it is usually very easy to do. But if your car is taking a long time to warm up and the engine gets cold while driving those are signs that definitely point to a stuck open thermostat.
Oh and as far as prepping your bumper for tape I have always either used a product called "Total Prep" which comes in a spray can or Acetone to clean parts prior to painting them. The Total Prep spray is a little milder than acetone but fair warning either one might take a little paint with them, but they leave a nice clean greese free surface that your tape should bond with very well.
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-Kevin
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