Reading so much different information, I decided to look at peppers the same as people. None of what I am about to say is concrete cause so many sources contradict each other. Here goes.
If a plant is cross pollinated, the children (seeds) will be a combination of mama and papa dna just like people. However, the pod of that plant will be pure mama dna like a woman's afterbirth. However, there is some scientific studies which have found papa dna in the placenta. So it is possible that the folk stories about changing heat via cross pollination might (might I say, might) change the heat because a lot of that is in the placenta. However, most folk believe it will not change the heat or flavor and the studies I have read were on animals, not plants.
Cross pollination should not change the shape, color, or size of a pod. That is all mama dna. If a black man gets a white woman pregnant, the baby (seeds) might be black but the mama wont turn black. This one I am absolutely sure of. The placenta might change, but not the outside of the egg / pepper itself.
A self pollinated flower will not contain the same DNA as the mother.  It contains a recombined DNA of the mother. If grown out / stabalized her dna is such a small variety that her pods will be about the same in appearance, but it is never exact dna. Again, just like with children, they dont all turn out exactly the same even with the same mother and father.
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But please do not think I am an authority on this stuff. I am only scratching the surface of cross breeding. So many folk wiht so much more knowledge.Â
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