Even if the temperature of the meats rises to the "danger zone" between 8 and 65 degrees celcius, it will still safely keep without refrigeration at all for at least two hours (Note this is two hours in the "danger zone" IN TOTAL).
If you can, bring ice packs (this may mean you can't bring it in your hand luggage). But if it's a stew type dish there's not a lot of added value to them. It might survive just fine. Do make sure to isolate it as well (wrap some towels and foil around it or whatever). For reference, my brother managed to transport cooked beef rendang all the way from Indonesia to Holland this way. If you can, pack a button thermometer along with the dish as this will help you get a clue on whether the food has survived the trip.
Finally, how you prepare and store the food makes a difference. If the food is sealed airtight while boiling hot (or at the very least over 80 degrees Celsius) then quickly cooled down after sealing, there won't be any live bacteria in there and it should survive for long without any refrigeration whatsoever (as does canned tuna).
A container that's airtight would be best, but another way is to use a rigid container and fat. Some traditional dishes such as confit of duck will keep without refrigeration because there's a layer of melted, set butter or lard on top of there which gives you that airtight seal that prevents any nasties from getting in. You can simply discard that fat once you've arrived.