Norwegian’s heat issues stem from an unusually high passenger capacity aboard the Boeing 787-8 jetliners that the carrier uses on its Las Vegas routes. Most airlines operate the plane with an average of 200 seats, but Norwegian puts 291 seats for sale on the 787-8 aircraft to keep costs down as part of its low-cost model.
Given the weight of those additional Norwegian passengers and all that accompanies them, the airline this summer found close to 300 people on board, including crew, and its planes’ ability to take-off during high-temperature periods was sometimes limited.
You see that Norwegian carries more people compared to other 787 operators. And they do indeed cite the passenger count as the reason.
Hot and high limitations are explained here, the biggest limitation for twin-jet planes such as the 787 is the ability to climb if an engine fails during takeoff.
The longest runway at Vegas' McCarran International Airport is 14,512 ft; the elevation is 2,181 ft.
From the 787 performance dispatch manual at 2000 ft pressure altitude and 42°C outside air temperature, we find the limiting factor is the climb limit weight, which is 195 tonnes (429,000 lbs).
The 787-8's maximum takeoff weight is 228 tonnes (502,500 lbs), that's a structural limit.
The 33-tonne difference is equivalent to 300 passengers (80 kg adult + 30 kg luggage and carry-on). Of course the plane won't be fully fueled, despite the huge distance, but you see how big the limitation is.
It gets even worse above 42°C. 30°C seems to be ideal. Vegas record high is 47°C, and the mean maximum in July is 44.7°C.
Why not depart from Vegas at night? Most probably due to slot restrictions. Waiting for the sun to go down means financial penalties, which is confirmed by the German news article.
Several times the airline had to move the flights to the cooler hours. It costs.— Google Translate
Vegas to Europe is a huge distance, and a direct-flight without a technical stop to refuel is Norwegian's only choice—evidently and understandably. Their low-cost model that favors filling all the seats over fuel is the limiting factor.
(gcmap.com) The four Norwegian routes, they range from 4,462 NM to 4,701 NM, London being ~4,600 NM.
Fully loaded with payload, the range is limited to 2,700 NM for a takeoff from a 42°C Vegas.
18 tonnes are to be shed to make it to London, i.e., 163 seats will be empty, or 90 empty seats plus leaving behind 8 tonnes of freight—airlines do depend on freight for profit. So, the typical quoted 200 passenger capacity would work. But if Norwegian doesn't do freight, then they're not to blame for cancelling the four European routes during the summer heat.
Boeing PDF on how to read the payload/range chart.