There's good news! You can buy Egyptian cotton blankets that stay cool or keep you warm depending on your choices. There are only two basic factors you need to understand to find the one that best fits your wants and needs. Weave and weight.
Weave, Warmth and Egyptian Cotton Blankets
Some weaves are tighter than others. How tight the weave is or the thread count can play a major role in how well something maintains heat. The looser the weave or lower the thread count, the cooler it will be. The tighter the weave or higher the thread count, the warmer you will sleep. In most cases, you can simplify the process of just paying attention initially to the weight of the blanket.
Weight and Warmth.
Although my claim above is true, there are other factors such as the type of weave as mentioned above. When you combine the two, you can go further to the extremes of cooler vs warmer sleeping.
Weight is an obvious factor. It makes sense the heavier it is, the more warmth it will have because the fabric is heavier, but throw in a tight weave and you get a very warm blanket. If you want a cooler blanket, go for lighter and a less tight type of weave and a lower weight blanket. Just take your time and look at the post about Egyptian cotton blankets on sites similar to this one on Luxury of the Pharaohs and you can find lots of options and designs that will keep you warm or cool while you sleep.