>I am using a USB bluetooth key on my ultrabook to allow me to use my own keyboard and mouse. As the temperature is rising, heath wave for five days, I see that the connectivity of the mouse to respond is not as good. So, basically, I have to get the ultrabook closer to the mouse during the day. At night, as the temperate is lowering, I can put it back to its normal location and everything works ok.
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>As those devices have their own CPU built-in, they seem to be somewhat affected by that. They do not have any fan so that might explain.

Extremely unlikely. Bluetooth peripherals typically use very low-power System on Chip (SoC) technology that draw mere milliwatts of power. They will not heat up even under continuous use.

If you check the specs for your mouse you will find it has a rated operating temperature range, with a top end likely to be 40C or even higher. With a safety margin the SoC and other internal components will be able to handle temperatures even higher than that.

It's possible your mouse is substandard but in that case I'd expect it to stop working, rather than suffer decreased range.

Computer equipment is a cutthroat business and to minimize costs parts are often shipped with ultra cheap no-name brand (and sometimes counterfeit) batteries. At higher temperatures the internal resistance of batteries may rise so output voltage may drop below spec. Or, the batteries may be getting low, you could try a new set of a good name brand.

If not that, I'd think it more likely something in your environment is causing that. Bluetooth runs in the 2.4GHz band and is subject to many of the same types of interference as WiFi (you can Google causes of WiFi interference). Maybe in hot weather there are extra air conditioners running, or they run continuously rather than intermittently, and generate extra electrical interference.

Or maybe when it's hot you place a cold drink on your desk and it happens to be between the mouse and the Bluetooth radio in your computer.

With all the above you can see why I'm a huge fan of wired peripherals, I don't tolerate any lack of reliability or precision in my keyboards and mice.