Keeping a small item refrigerated in carry-on on short domestic flights

My next trip is composed of two domestic flights with a short connection. I will be travelling with carry-on luggage only, containing cheese that is best kept a fridge temperature.

What is the best solution to keep it refrigerated during the whole journey ? Time from fridge to fridge is about 5h.

• My current fare does not include checked in luggage
• Ice packs may be allowed (company website does not list them in forbidden items), but I'd rather avoid freezing the cheese
• There is some leeway in the temperature, no need to keep it at a constant 3°C. Anything below 8-10°C should be ok.
• Cheese size is ~10x5x5 cm

EPILOGUE

First trip - Joe Blow was right, the cheese was denied boarding by security. Had it been sliced first it would have made it through.

Second trip - I wrapped two of those cheeses in a thermal bag, and checked the suitcase that contained them. While I had ample time at the connecting airport to board my second flight, the baggage did not. The last flight was late at night so the cheese spent the night at the airport, only to be delivered in the morning. It was still slightly cold (so was the night in early November) and perfectly edible.