i would suggest a stainless steel flask aswell , put some insulation inside a pannier, an ali pannier would be better as it would reflect some heat and just apark in the shade, should be good for a day or two .
Other ideas is there an alernitive drug ? get in touch with the drug manufacturer , they may say it's ok upto a higher/cooler temp as long as it is cooled/heated before use. Try and find a good pharmacist to talk to, it's amazing some solutions they come up with.
Another spanner in your works, on the round the world trip get a note from your Dr detailing your medical problem and what drugs have to be taken and make sure that these are readily available where ever you aim to go .
If you take a load of prescribed drugs over a border you best make sure you have all bases covered , otherwise you may have free accomodation in a secure compound !!!!
There is always a solution enjoy your trip