They said: "The bathroom had run out of toilet paper. One young boy became nauseous and was trying to make his way to the bathroom when he vomited in the aisle and all over several passengers two rows behind us.
"The stench was unbearable."
At one point passengers chanted "open the door, open the door" to cabin crew as the temperature on board reached more than 31C.
After calling 911, passengers were given water by emergency responders.
Air Transat blamed circumstances that were out of its control, including long waits for fuel.
Airline CEO Jean-Francois Lemay said on Thursday that "something did not work well, obviously" on 31 July.
"I am not saying there is a fault or blame but there is a collective responsibility that has to be observed in these events."