The Euclid's data sheet says that it can handle a maximum of 35 degrees external air temperature.
I was not sure whether you meant that it was 75 degrees weather in your location or 75 degrees temperature inside the Euclid's casing.
If it is inside the casing, it sounds like you are running a program that is pushing the Euclid's processor chip very hard and radiating a lot of heat from it, causing shutdown because the cooling fan in the Euclid cannot cope with it.
What is the weather like in your location? Hot weather and / or thin air (e.g in high mountainous locations) can cause a fan to struggle more than usual. A symptom of a struggling fan is it making more noise than usual as it works harder to try to keep the processor temperature down.
Also, Ubuntu's 'System Monitor' window could show you what processes are running so you can see what is causing high processor load.
The external temperature (ambient) is roughly 28-30 degC
The temperature of 75 degC is read in the Euclid interface (10.42.0.1/#system/status) : “System status” in “Utilities Tab”
This morning temperature in France is lower (20 degC), but the Euclid don’t start! There is just a big fan noise…
Is it possible to burn the Euclid just by playing the prerecorded scenario with the Turtlebot?
The shutdown mechanism when the internal temperature becomes too hot is designed to stop damage being done to the hardware by giving the device a chance to cool down. So if the shutdown mechanism is working correctly when temperature becomes excessive then there should not be permanent damage. If the temperature rise is sudden though then this is not a guarantee of avoiding burn damage.
Years back, I was working on upgrading a Celeron PC with the casing open and had the processor instantly burst into flames on startup because I hadn't seated the processor's pins in the socket properly! An extreme example, but it killed the processor because there was no way back from sudden heat death like that.
If the Euclid were working correctly then if it thought the temperature was excessively hot, I would expect the BIOS to automatically shut the Euclid down, not stay on with the fan running. That symptom does not sound encouraging, unfortunately. If you need to return your Euclid to Intel for refund or replacement, you can do so by emailing email@example.com