I put a battery (3 cell 11.1 V) in one Arduino pin, but next to the Arduino (believe is the transformer power) a black box is heating up too much.
This is normal, or if I leave it on for a while the Arduino can burn?
Yes it is normal and yes you can burn out your arduino, or more specifically the black box voltage regulator ( it is not a transformer ).
This is because it is being asked to burn off too much current. Drop the voltage to something lower but above 6.5V.
You might want to edit the part where it says burn off too much current.
Hi henrique-rafael
I think you must be connecting some components to the Uno that draw a significant current, such as a bunch of leds, correct?
You could consider using a dc-dc convertor to power the uno from your battery. They are much more efficient and will not waste battery power as heat. You can adjust the output of the convertor to 5V and power the Arduino through its 5V connector instead of through the power jack.
Paul