Is the inside of the flight case metal, or is it lined with something? If you have a decent amount of inside air exposed to the metal then the flight case won't get very hot inside.
A really easy non-technical experiment would be to put the Bela + BBB in the tupperware and leave it powered for a couple hours. Come back and touch the tupperware.
If the tupperware is only warm to touch, it's probably ok. You can take it a step further by taking it out of the tupperware and immediately stick your finger on the top of the CPU on the BBB. If it's uncomfortably hot, then you should poke some holes in the tupperware. If you can hold your finger on the CPU without discomfort you have nothing to worry about and you can leave it all sealed off.
Just making sure the tupperware box has good contact with metal in the flight case could make a notable difference. Another thing could be to wrap the tupperware box with aluminum foil with a crumpled outer surface (maximum surface area to air in the flight case. These are simple things that don't require making holes.
Ultimately this is a thermal conductivity and heat capacity consideration. If thermal conductivity was, say, 20C/Watt, then the air inside the tupperware would eventually end up at about 50C higher than the surrounding (outdoor) air temperature. This would be ok, but not good for long-term reliability.
Heat capacity consideration defines how much time it takes for the BBB to reach the final temperature. For example, it may have the 20C/Watt thermal resistance, but it might take 3 hours to get there, so operating for 3 hours at a time this would not be a problem since most of the 3 hours would not be very hot.
Finally, outdoor temperature will make a difference. It might be ok when it is 20C outside, but is it ok when it is 35C outside or if it is exposed to direct sunlight?
You can keep sheltered from direct sunlight, but if you operate it on a hot day, you should take it out at the end of the event and stick your finger on the CPU to see how hot it gets.
A thermocouple is more scientific, but you will know it is operating at a safe temperature as long as it isn't uncomfortable to touch the CPU.