This is likely something you need to determine experimentally. You can probably get some idea from other BGA devices as to what sorts of ranges work for this if you don't have a stack of PS3 boards to try it out on.
We don't know what machine you have
We don't know how it is calibrated on the temperature front (is it temperature at the tip, at a distance of 500mm...) or whether the probe it uses is any good.
I don't know if the PS3 varies in CPU or GPU thickness between different models which means different times heating.
I don't know what you have done for pre heating (most will suggest you pre heat the board before playing with IR reballing stations).
I don't know what you are doing for shielding the surrounding components, and indeed if they are a few passives if you don't mind replacing/reflowing then that might be a tradeoff.
I don't know what you are doing for flux here -- that could conduct heat better and prevent certain issues.
I imagine it uses nasty lead free solder so you have that to consider (lead free tending to be higher temperature). Something to keep in mind if you reball it with nice leaded solder balls and need to redo it later as well.
Lower temperatures mean longer times but also more risk the heat will spread. Too low or too short or too slow grabbing it after you turn the heat off and you might rip off BGA pads as well which is no fun at all to try to fix.
Higher temperatures mean shorter times but also more risk you burn something nearby or under it, to say nothing of most components only have a few times they can be cooked before they fail in odd ways.
https://www.petervis.com/Education/...ectronics_Students/Soldering_Temperature.html has some temperatures for known solder types, but you would probably want to go a bit higher to account for losses going through the chip itself and so it does not immediately refreeze after you reach in with the pincers/suction cup.
is this tool can use on heat gun tool machine or must the reballing machine.. To work fine safe.. 
