The child, who has not been formally named, was reported to have entered the water at Tagg's Head Island in Hampton, west London, at about 16:40 BST.
Searches were carried out by police, ambulance crews and the fire service, along with members of the public.
The search was called off at 18:40 BST but efforts to recover his body will continue into the night.
The boy's next of kin are aware and are being supported by specialist officers, the Metropolitan Police said.
Supt Richard Smith, from the Met's South West Command Unit, praised the efforts of all those who tried to find the teenager.
"Despite the very best efforts of all involved, we must now sadly conclude that this young boy has died," he said.
"His death is a tragedy and I cannot begin to imagine what his family will be going through. All our thoughts are with them.
"I know that on days like today when temperatures are at a record high, it might look appealing to jump in and cool off in rivers, reservoirs, lakes or other open water.
"Please don't. The dangers are real and this evening we have seen the terrible consequences of what happens when it goes wrong.
"To young people in particular, I would urge you to be the person in your group of friends who says no and reminds others about the dangers.
"Your intervention could save a life and save another family from experiencing such an awful loss."
London Fire Brigade's assistant commissioner Charlie Pugsley offered an additional warning to those tempted to swim in rivers during the heatwave.
"Anything below 15C is defined as cold water, and on average the UK and Ireland sea temperatures are just 12C. Rivers such as the Thames are colder - even in the summer," he said.
It follows a number of similar deaths in open water in recent days.
A 16-year-old boy died in Bray Lake near Maidenhead, Berkshire, a 13-year-old boy drowned when he got into difficulty in the River Tyne in Northumberland on Sunday and a 16-year-old boy died in Salford Quays, Greater Manchester on Saturday.