It's a perennial problem with the BA 400's I'm afraid, don't know if other operators have the same problem but it's always seemed to be that on the ground the aircraft's own A/C set up on the 400 is particularly gutless and the ground conditioned air at Heathrow T5, if used instead of the aircraft packs isn't particularly great either.
Possibly it's all down to a general fore to aft flow of air through the aircraft plus the considerable amount of heat generated by the Inflight Entertainment System and lights, plus the heat generated by the passengers themselves as they move around during boarding. Certainly once the rear zones (compartments) get hot on the ground there's little we can do to cool them down until we get airborne. Once airborne in the cruise the temperatures in each zone can be controlled individually and should be easier to control. In extreme cases of zones being hot in the cruise we can increase the flow of air through the system temporarily to drive the Cabin temperature down to more comfortable levels...