Is there a connection between heat intolerance and asthma?

Yes. Heat intolerance (i presume more than usual) relates to abnormal adaptation and isperceived in the lower part of the brain. An unbalanced signal through the autonomic system to the bronchial tubes causes asthma. Both are related to inefficient metabolism in brain. Commest cause is "junk"diet. See my blog "oxygen the spark of life" that you can google.