I don't know the temp after a Gen3 SC only my Gen5.
Normally under 0 boost conditions when the bypass is open, my air is heated from 50 F IAT to 120 F.....or from 80 F to 150 F so about a 70 F rise.
Under boost when the bypass closes, the temp rises another 50 F for a total of 120 F rise over intake air temps.......so if the IAT is 50 F, at full boost I am seeing 170 F after SC temps.
This is with a 3.2 pulley at 13 psi boost.
If you draw your intake air from the 130 F engine bay, your after SC temp could be 240 F.
..............and this is with a Gen5 and 160 stat.
I can only guess that a Gen3 with 180 stat would be 20 - 30 F ??? warmer.
Flesh scalds at 140 F.
I believe that Bill Boost also runs an after SC temp sensor but he has not given up any info......that I have read.
....remember that for every 10 F lower temp you will produce 1% more power, so if you can reduce the temp by 80 F you will gain 8% more power.
....but more importantly, you will be able to drop pulley size for more boost pressure and more power. I think 1 psi is worth about 5 hp.
The PCM will advance timing for more power. 1 degree is 3 hp.
It'* all additive.
It'* all good.