We always take-off with the packs selected to off. This is to reduce wear at the third stage of the compressor (or something like that). Basically it's a cost saving.

If it's really hot in the cabin, then the packs are run from the APU. If the APU fails during the take-off run, the FADEC compensates by running a slightly higher EGT to preserve perfomance integrity.

A4:)