It may never overheat if you have one of the new models that use less power than the early fat models. The PS3 does not void a warranty for playing continuously night and day and many owners have done so.
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The ps3 slim doesn't overheat
the ps3 can over heat but it really wont unless you block the air vents
it means the connection on your ps3 is low or even if its high it hasn't picked it up properly yet if you wait a while it will sign you in if it doesn't it means there is a problem with your ps3 connection if it still says it in about 3 weeks it means your ps3 could be starting to overheat like my ps3 it will later on get the flashing red light so to prevent this TAKE YOUR DISC OUT OF THE PS3 WHEN DONE!!!!
It has a cooler causing it to never overheat as many have said.
It should not take long, if you are having trouble see related questions answer