<<Disclaimer: Verify this information before applying it to your situation.>>
 
Antibodies are known to sometimes cross react with proteins having segments
(amino acid sequences) sililar to their original intended target.   Perhaps
heat intolerance in celiacs could be caused when antibodies triggered by
ingested grain proteins cross react with regulatory proteins (for example,
proteins that regulate the opening of skin pores, etc.)   This would
explain why such a reaction could be either excess sweating in the absence
of heat stress or lack of sweating in the presence of heat stress.
 
It's also conceiveable that the antibodies could be cross reacting with
other heat shock proteins.
 
If either were the case, the degree to which reactions were altered would
be expected to be related to the amount of triggering protein ingested.
 
Perhaps the "leaky gut" in celiac is also caused by cross reactions of
antibodies with regulatory proteins.  (The action of a protein that
expanded a skin pore seems similar to one that opened the spaces between
cells in the gut -  maybe simialr proteins could be involved which are also
similar to proteins in grains ((which could be also regulatory proteins
evolved from the same ancestor proteins as the human regulatory
proteins))).
 
Please note:  The above is rank speculation!  Sometimes I just like to
speculate.