Answer: Cross pollination of sweet and hot peppers will not affect the fruit characteristics of this year's plants. The seed from the cross will be a mixture of the two parents.
Pepper pungency, even in a jalapeno, can be kept to a minimum (within the pungency range for the type of pepper) by minimizing stress. That means providing plenty of water and fertilizer. Too much fertilizer will reduce bloom and fruit set, though.
I think some mislabeled banana pepper plants (there are both hot and mild types) have helped perpetuate the myth of cross-pollination affecting pungency.
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