How to keep warm arduino uno board with 12v dc supply
See Can I use arduino&#39;s 3.3 V output directly to esp8266?

From that page:


  The specs for the Uno say that it does not provide as much current on the 3.3V line as the specs for the ESP8266 requires. You will need to provide another regulator that can supply enough current.


Also, putting 12V into the barrel jack is making work for the on-board voltage regulator (located near the barrel jack) because it has to convert 12V to 5V (making heat in the process). You would be better off putting a lower voltage into the barrel jack, ideally around 7V (but not lower).

Alternatively, just power through the USB port as you have been, and plug the USB cable into a USB charger.



To summarize, both the 5V and 3.3V voltage regulators are probably working very hard, thus getting hot.