The English end of the Folkestone-Calais link was worst affected, with travellers forced to queue for up to 90 minutes just to check in and a further three and a half hours for the next available slot, according to the operator.
Footage posted on social media showed long queues of cars, caravans and lorries.
A Eurotunnel spokesman said: “Due to the exceptional and prolonged temperatures, some of the air-conditioning units on board our shuttles are struggling to produce sufficient cool air.
“Our priority is customer well-being and safety so we are unable to board vehicles to these carriages.”
Passengers were advised to take plenty of drinking water and find toilet facilities before arriving.
Temperatures in Folkestone were expected to reach 31C on Thursday.
It is one of the busiest weeks of the year for Eurotunnel as the start of many school summer holidays leads to a surge in families travelling to France.