A CHE takes a long time to heat up and cool down. Make sure you use the proportional mode on the tstat.
Also aCHE calls for certain types of fixtures. Make sure you get the recommended style. Failing to do so will cause the CHE to burn up and you will waste your money. I have one going on 11 months of constant use.
I really would not suggest placing the fixture directly on the tub. I would find some way to suspend it our give it a stand off so it never touches any plastic.