Apple - 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.
I found the center pin on my charger was "pushed in"...recessed and not protruding like the other 4 pins. Pulled it out with a needle nose plier & cleaned all contacts. Now working.
I also found that spinning it around, 180 degrees, fixed the issue. Not sure why but looking at the female side of the adapter it seems two of the connector pins on one side are closer than on the other side. I also maybe hallucinating.