Hi,
Can you please post a copy of your circuit, in CAD or a picture of a hand drawn circuit in jpg, png?
How are you powering the 5V peripherals?
If you are using the 5V pin of the UNO, then when you have the PC plugged in, it is supplying the current for the 5V devices.
When you change to a 12V input, you are using the UNO internal linear 5V regulator, this device is limited in how much current it can regulate.
It sounds like it goes into thermal shutdown because of the current it is supplying and the 12V to 5V differential across the regulator.
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A solution is to use a 5V supply connected to the 5V pin of the UNO rather than 12V to the DC socket.
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Reducing the socket voltage from 12V to 9V may help, but it may just prolong the agony.
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12V to the DC socket and a separate DC-DC converter 12V to 5V, would be better, the converter supplying 5V to the peripherals.
Tom... ![]()