Cargo for animals really is very good. The heat is an issue, obviously, but they won't fly the animals if they can't keep them comfortable at all times during the journey.
I haven't done the flight UK to US, but back in March my cats flew Virgin from Heathrow to Wash DC and were just fine. As a matter of fact, they were so NOT traumatized by the whole event, they just sauntered right out of their carriers as soon as we got them home. We've moved house before, the car drive was more stressful for them than the plane!