I haven't tried this myself, but there is a case made to keep insulin cool for diabetics that might work for an Epipen. It is made by Frio. Do a google search for the term "Frio wallet" and you should find a number of sites that carry it.
From this link
http://coolerconcept.com/pages/faqs.htm
WHAT TEMPERATURE DOES A FRIO® WALLET MAINTAIN?
"We hate to sound redundant here, but used properly an activated Frio® wallet will have an internal temperature between 60°F-72°F, depending on the climate which the wallet is exposed to."
CAN THE WALLET BE USED FOR OTHER MEDICATIONS?
Yes, Frio® wallets can hold other medications. Epi-Pen (epinephrine) manufacturer state that their pens do not require refrigeration, but must remain in the temperature range of 59°F-86°F. It is imperative that you contact your Doctor or the manufacturer of the drug you would like to carry in a Frio® to ensure that it will be at the correct storage temperature inside a Frio® wallet as further tests other than insulin have not been undertaken at this stage.