The part of the Arduino data sheet that Clearly you didn't read is the part about recommended loads for the Arduino board or any of the recommendations here.
Or about the shield you are using.
Try to remember that ALL of us here that answer these questions are just people and that we had to find your answers the same way you should.
You might also search the forum for your shield too as it's power requirements are likely addressed as well including solutions to what is a VERY common issue that I tried to address for you with the few small suggestions I made.
I am not really trying to be a hard case about this BUT You have to do part of the work your self.
Did you know that you can search this forum for answers and that the search will return a value for relevancy?
If you Search for "regulator heating" in about 20 seconds you will get 5 pages of answers.
Read them and follow the idea's and suggestions there as well as any links or other information.
If you still have unanswered questions then come back and ask them...
I am reasonably sure you will find the answers you seek long before you need to ask for them here again.
I am also sure that there will be other questions to be answered as well
Again search and then if you found no useful answer...
Please come and ask to see if someone has a solution.
You will never learn if you ask first and read second.
All you will learn is how to ask...
What if one day there is no one to ask?. What then will YOU DO?.
Doc