Egypt has four travel seasons that matter for a trip, and each one has a cost. They feel different once you are standing in them, and the honest version of each includes the downside.
Autumn: October and November
Autumn is the season to start with. Temperatures settle into 22–32 °C, which is 72–90 °F, and the drop from summer is the first thing you notice. The pattern is stable, sunny, and dry, which is what you want when the plan is three outdoor sites a day.

October and November suit Cairo and the Nile Valley. The scorching heat has gone, and the winter chill has not set in, so a morning at Giza happens at a temperature your body can work with. The Red Sea coast is still warm and still good for water.
Tourist numbers climb quickly from mid-October, and that is the catch: Nile cruise cabins and good hotel rooms tighten first, then the price follows, so the river is the piece to lock in early. It is comfortable here, not quiet, and comfort is what pulls the crowd in.
Winter: December to February
Winter asks the least of you. Daytime temperatures in Cairo and Luxor average 18–25 °C, or 64–77 °F, which is close to room temperature, and rainfall inland is minimal to non-existent. You get dry, sunny days and a sky clear enough that photographs of stone come out with detail instead of glare.
Does the cold matter? At noon, no. After dark, yes. Nights in Cairo and in the desert drop as low as 10 °C, which is 50 °F, and buildings built to shed heat are not built to hold warmth. A jacket earns its luggage space, and so does a layer you can shed by ten in the morning.

Expect maximum crowds and the highest prices of the year for accommodation and cruises, with the sharpest spike around Christmas and New Year. In exchange, you get the most dependable weather of the year for the classic route of pyramids, river and tombs.
Winter also suits anyone who wants long days outdoors without paying for them in exhaustion. The Valley of the Kings is the test: a sprint between shaded patches in July, a morning you can take slowly in January.
Spring: March to May
Spring is a shoulder season: warmer than winter and quieter than summer. Temperatures across the country run 20–32 °C, or 68–90 °F, and the days are generally sunny and dry.
The catch is the Khamsin: a hot, dry, dusty wind off the Sahara that can last a few days at a time. April is when it shows up most often. When it arrives, visibility drops and the pyramids go soft behind a sheet of dust, so outdoor sites are better pushed to the next morning.
April still works because the wind is episodic, not constant. Most spring days are clear, and the rest are obvious by seven in the morning. Build slack in: if the dust comes, move the museum visit forward and push the outdoor site back.
May is usually the last comfortable month inland, in Cairo and Luxor, before the heat settles in. On the Red Sea, water temperatures warm through spring, which makes March to May a strong window for diving and beach days before the worst heat.
Summer: June to August
Summer is the off-peak season inland, and the heat is the reason. Temperatures in southern Egypt regularly exceed 40 °C, which is 104 °F, and desert areas go higher still. Cairo averages over 34 °C, or 93 °F. Daytime sightseeing at ancient sites turns exhausting, and through the middle hours it is not worth attempting.
The coast is a different country in the same months. Sea breezes temper the Red Sea shore, where average highs sit around 32 °C, or 90 °F, and the water is warm and clear. That makes June to August a diving and snorkeling season rather than a temple season.
Nile cruises and inland tours drop to their lowest prices of the year in summer, and the pyramids come with a short line at opening. If you can handle heat and want the sites without shoulders in front of you, that is the deal: out at dawn, indoors by noon, back out in the evening.