"It may have been 80 degrees outside, but I put the bottle in a cup of ice to keep it cool while I walked."
Not a problem, no harm done at all. The ice should have kept the temp well below 80 F, down somewhere in an acceptable "room temp" range at the highest.
From the label of a $30 bottle of Metagenics 15 billion active unit probitics, and I think this would apply to many other refrigerated probiotics as well: "For maximum stability and viability, keep refrigerated. However, product may be stored at room temperature for up to one week without adversely affecting potency. Excellent for traveling."