Flying on Tuesday, I was surprised to board at LHR and find all the window blinds open and the sun shining through heating the furniture on that side of the aircraft. Having all the soft and hard furnishings heated up to 50 degrees + means that the air conditioning is not only cooling the air down, but also these furnishings that will act like efficient radiators for several hours. That is a cost cut that Alex Cruz missed out on. Bad Alex.
I am not aware at what point BA deem a hot uncomfortable cabin to become a hot unsafe cabin, but I wonder what the result would have been had the captain said something like: "It's 40 / 104 degrees on board. You can wait for an unknown length of time until we get it cooled or cancel the flight, or board and put up with it." and taken a show of hands. If the majority want to board now, anyone who wants to offload, can do so and take the next available flight which may be in a couple of days.