"The runway re-opened to departing flights at 17.40 (BST). Arrivals remain suspended until further notice," the airport said on Twitter.
Temperatures rose above 37C in parts of England and were forecast to hit new record highs above 38.7C on either Monday or Tuesday. Much of Europe has also been baking in a heatwave.
The airport, located around 35 miles north of central London, is used by airlines including EasyJet, Wizz Air, Ryanair and TUI.
Some 14 flights due to land at Luton were diverted to other airports including Gatwick and Stansted on Monday afternoon, according to FlightRadar24 data.
There were more than 60 arrivals and departures operated by EasyJet, TUI, Ryanair and Wizz delayed at the airport, according to a Reuters tally of the Luton arrivals and departures board online at 1600 GMT.
That total included 14 Wizz flights heading to European holiday destinations including Tenerife and Dubrovnik, and 16 EasyJet arrivals.
Britain's Royal Air Force said on Monday aircraft were using alternative airfields to its Brize Norton air base due to extreme temperatures, after Sky News reported that the hot weather had melted the runway at the Oxfordshire base.