I have replied with specific examples of how this done. Didn't you read them?
Here's a quote from one of several relevant links I sent you. Does this answer your question, or are you going to keep doing this song and dance in the hopes of dodging the inevitable bullet?:
HSP90 belongs to a class of proteins called chaperones, which help other proteins in the cell fold properly, prevent protein clumping, and escort improperly made proteins to be recycled. These vital functions become even more important when a cell is stressed by heat, cold, toxins or other hardships that affect protein folding.
Hsp90 is particularly interesting because it is specialized to chaperone proteins that are key regulators of growth and development. Thus, it is in a position to couple environmental change to the release of hidden genetic variation and thereby to produce a host of new traits.
http://www.sciencedaily.com/releases/2008/02/080223123054.htm
Methylating/demethylating DNA turns genes on or off it doesn't change what proteins they make. That is accomplished through mutation.
Nothing you have sourced contradicts this. You have proposed an epigenetic model to explain the emergence of heat tolerant proteins from non heat tolerant proteins but cannot explain how the heat tolerant protein was produced through DNA methylation and not DNA mutation.
Do you even understand the difference?