My MagSafe to MagSafe 2 converter becomes extremely hot. Why?
Actually it should be RT (room temperature) like all the time. 

Check the pins to see if one of them is getting discolored.

The only reson for your converter to get hot is a bad contact creating a arc, that creates heat.

Making sure the plugs sit tight (on both sides) and that none of the contact pins (on both sides) is discolored. Cleaning the pins could not harm.

Ultimately getting a new converter would be a good idea.