mine is the same way
it's an inline old style automotive type tube fuse
and yes it gets very hot.
I thought I had a picture of it, but can't put my fingers on it at the moment.
When we first got it and I noticed how hot it was, I had also noticed that sometime along the way those little tiny wires had been pinched in the swinging mount along the way. Eventually, that TV died and the dealer replaced it under warranty and when they replaced it they upgraded the wire a bit to a larger gauge. It's still small and still gets hot, but it functions well and hasn't so far been a problem.