Hi cbcb,
Generally the most popular cover for a memory foam mattress would be some type of stretch knit material that doesn’t interfere with the compression of the memory foam under it and allows heat to go through it but there are also many other options and some people prefer a cover that is quilted with a more resilient material such as polyfoam so that the sleeping surface is a little more resilient and breathable and the memory foam is a little more motion friendly.
It really does depend on your personal preferences and which type of “feel” you prefer in a memory foam mattress along with the specifics of the mattress design.
The type of cover in your mattress (and the materials in the quilting if it’s a quilted cover) can also play a significant role in the sleeping temperature of a mattress and natural fibers (such as cotton, wool, or linen) or semi-synthetic viscose types of fibers (such as rayon, bamboo, tencel and others) are very good at wicking away moisture and helping to regulate temperature and some of the engineered fabrics (such as Coolmax or Outlast ) can also be a good option to help with temperature regulation.
In most cases though … a thinner stretch knit cover is the most popular choice because it has the least effect on the memory foam and provides more of an “in the mattress” feel which is what many people like about memory foam. Of course if you like a mattress then the cover that goes with it isn’t really an option but it may affect the choice of a mattress because a cover can play a significant role in the feel and performance of the mattress.
I would also be aware that the cooling properties of gel are often a secondary to its ability to improve the support qualities of memory foam and to help prevent it from sinking in too far over the course of the night (and the sleeper ending up with a back ache from sleeping out of alignment). This is why you will often see gel memory foams in the middle layers of a mattress under regular memory foam. You can read a little more about some of the factors that can help with temperature regulation in a mattress in post #2 here and about some of the technologies used to help memory foam sleep a little cooler in post #6 here. There is also more information about the different types of gel materials that are being used in memory foam and other types of foam in post #2 here.
If you are talking about a mattress protector (instead of the mattress cover or ticking that is part of the mattress itself) then there is more information about some of the different types and the pros and cons of each in post #89 here and the posts it links to) and my apologies for including information about mattress covers instead of mattress protectors 
Phoenix