All Egypt routes SSH Marsa Alam HRG LXR and even the most south Aswan are all no problem for a full 737NG (700 and 800) on most days from/to most UK airports
Egyptair use a 737-800 on the Luxor Heathrow route every Monday (2500 miles) and during September the temperature can reach around 40+c at departure time. So imagine the the weight and runway length needed for that.