I use Copaxone, which is able to come to room temperature. But I do travel with a small gel pack to keep it from getting too warm. Just make sure you have the prescription label with it, and I would get a doctors note as well since you will be taking such a large quantity with you. Check with the airline to make sure you can carry that much on; if not you can check with Avonex to see if they will ship it to you down there.

I travelled with partner (and his Avonex pens) and had to plan it myself. We used to backpack before his diagnosis and travel really low budget anywhere. We decided to keep doing it as long as it was possible. Last trip was for a month in Vietnam. I got cooling bags calling the Avonex helpline (the NHS later sent us a cooling bag and a practical carrier bag too). They carry 4 doses, but I reckon you could fit more removing the pens from their boxes. Since they only keep the temperature for 24h I had to book the first night in a little hotel with mini bar where to store it after the long flight. I also contacted private clinics throughout the country where we left and stored the pens and later collected them according to need. People was really supportive. That allowed us to freely travel exactly how we used to do! Make sure you bring a small thermometer to keep near the pens all the time to check fridges and cooling bags temperature. Good luck and enjoy your travelling.