What could have caused the burnt electronics smell in my Kenmore washer and dryer?
I have had a few control boards from assorted appliances burn to some degree, but continue to function.

Those pc boards tend to be made from bakelite, the brown color boards you see in less expensive items. Bakelite is a paper based product.

And it smells 'that' way.

If there is loss of heat from the dryer, it is likely the board that controls the temperature. The boards are behind the control section of the appliance, and the ones I have worked on have always been easy to replace.

Buying appliances that are sold by Sears, is great because they stock parts from many years back.