Zelly, a grim story and PPRuNe is the right place, and this forum is now probably the right one. Don't stop writing to BMI. Write to the chairman's office and let them know that you have broadcast the information in the internet. If they don't reply, send the letter Recorded or Special Delivery to get a signature.
Go to
BBC Watchdog (no pun intended) and let them know. Send them copies of the letters and exact details of the date, times of the problem and the sequence of letters/calls in the ensuing months.
The Watchdog pages states: "Do you have a consumer complaint that you would like Watchdog to investigate, or do you have a comment about the programme? If so, choose a subject below, then fill out the form leaving details of your story." Your concern would probably fall under 'Transport' as there is not one for pets.
I was departing LHR on 8th August last year, two days before the 100F mark was reached. The a/c was delayed by a technical fault and the ground air handling unit could not keep up. We sat with sweat rolling down our faces for 40 minutes. For an animal that was alone and without special care - it must have been ghastly.
Do let us know what happens.