One thing that most people do not realise about the temperatures in Egypt is that the winter months can drop very low, which does mean that warmer clothing should be brought, especially when on a Nile cruise. Winter also brings rain, though the amount does vary from very wet in Alexandria to just a few hours over a few days in Cairo and to the south (Luxor and Aswan have hardly any rain at all).
Humidity is another factor to be taken into consideration. Whilst it is very high in coastal regions, including the Red Sea, the Nile valley has hardly any, though it has been slowly increasing in Cairo since the building of the High Dam in Aswan and so it does mean that it seems a lot hotter there than it used to be.
Wherever you are going to in Egypt, no matter which month you travel, you are always advised to ensure you bring sun protection, this is especially true if you are going to be spending many hours visiting the various ancient sites. Egypt is a desert country and so is mainly flat, which means very little shelter from the sun, so sunburn is a major concern, as is sunstroke. Sunhats, high factor sun creams, and any other forms of protection are a must: even parasols are getting more and more popular with some visitors.
The months between May and October tend to be a lot hotter than in the rest of the year, especially in Upper Egypt (basically anywhere south of Cairo) and the afternoon temperatures can easily exceed 50°C. This is especially true in the more desert areas, which just happens to be where most of the tourist attractions are situated (Abu Simbel is a prime example). These months mean that the best time to visit any sites are in the morning, before the sun starts its relentless shining, leaving you the afternoon to relax and/or seek shade in the many streets in the various cities you visit, or under the parasols in your hotel.
During the period from mid-March to mid-April the annual sandstorms, known as the Khamsin, arrives, though it is not as bad as some people try to make out. In reality it only lasts for a few days, and only for a few hours during those days. It is easy to cope with and many people do not even realise that it is happening.