I've been travelling for years with a biologic medication that needs to be kept quite cold. I've accumulated various types of small coolers including evaporative (no power required) and 12 volt powered ones. None of them really work well enough for me to to be useful over lengthy periods in hot weather.

I've defaulted to old fashioned frozen gel packs. I use a well padded camera bag to which I add extra layers of insulation. I fill it with lots of frozen gels including a type made by a company called Med Active which reliably stays frozen longer that the typical pharmacy types. I've used this arrangement in Sicily and in Africa under temperatures exceeding 40 degrees centigrade.

Of course, this arrangement does depend on spending every night, or at least every second night, somewhere where refrigeration (with a freezer) is available to use.

You haven't mentioned which type of medication you are dealing with. At least some biologics (e.g. Humira) are capable of surviving unrefrigerated for a significant period of time as long as the the temperature is below 25 degrees centigrade. Humira is good for 14 days. Hadlima, a biosimilar of Humira, will go for 28 days. This extends the travel friendliness of these medications considerably. I don't know what the situation is with insulin or with the many other biologics which seem to be flooding the market. Obviously it's key to check the data provided by the manufacturer.

On one motorcycle trip in very hot weather, knowing that I was going to use it soon, I simply kept an injector pen in a normal thermos bottle in which I also kept a small, ordinary frozen gel pack. I was confident that the contents would stay below 25 degrees for the required time.

A few years back a young engineer (in Ireland I think) posted here, I think, about a project he was working on to develop a powered cooler for motorcycles. Might have been on Advrider.

It's a hassle really but just a nuisance when you think about how many of these drugs are great scientific achievements.