Gotta agree with the heat problem... buy a can of air and clean it out a little perhaps?
I don't have an X-box but I do know that shortly before a computer overheats it will freeze for a few moments.

That would also explain why it gets worse as you restart it. Does it get better if you wait a day?

Just be very careful because repeatedly overheating an electronic can break it o.o

And to give a smile... I'll give another bit of tech support advice: