rca model f35750st turns its self off & on

I have an RCA model F35750ST.  It starts up great, but after a few
minutes it shuts itself off.  It will then turn itself on and off
a few times then stay off.  It seems like something might be
overheating creating the problem.  Any ideas?  Do you think
this is a part that we can replace ourselves or should we just throw
the set away?