Hi udoknowjac,
A mattress protector is designed to protect the mattress or any toppers under it from the fluids you release each night, from dead skin cells, from spills and accidents, and to keep your sleeping surface in clean and hygienic condition.
A topper cover is meant to protect a topper from oxidation, from damage with handling, and to some degree to exposure to substances that can harm it but they are not generally waterproof or water resistant so it’s usually a good idea to use a mattress protector over a topper.
I would tend to use both a cover for a topper and then a mattress protector over the sleeping surface. There is more about the pros and cons of different types of mattress protectors in post #89 here.
You could probably “make do” without a topper cover (although it may increase the risk of damage or shorten the useful life of the topper) but I would make sure that you have a mattress protector over your sleeping surface that can be easily removed and cleaned.
Yes … anything in between you and the mattress can affect temperature regulation in one way or the other including the fabric used for a topper, the topper material itself, your mattress protector, and your sheets and bedding. The better the moisture wicking and ventilation against your skin the better the temperature regulation will generally be. The post I linked earlier has much more information about the many variables that combine together to affect sleeping temperature and the relative benefits of different materials that you can use as a guideline in your choices if temperature regulation is your main goal. I would keep in mind that anything that you use over memory foam can affect the amount of heat that reaches the memory foam which can make memory foam that is more temperature sensitive feel firmer.
I would also keep in mind that if you add a thicker topper for temperature regulation (vs a thinner mattress pad or mattress protector) that it will also have a significant effect on the feel and performance of the mattress in terms of PPP (Posture and alignment, Pressure relief, and Personal preferences) and will do more than just affect sleeping temperature.
You are in a lighter weight range and appear to prefer the feel of memory foam so I would probably consider a more breathable and faster responding 4 lb memory foam or gel memory foam. 2" - 3" would be the most common thickness depending on how much more pressure relief you think you need.
I don’t recommend any specific brands since almost all the North American memory foam manufacturers make a memory foam that would be in the range of density and properties that was suitable for you. Instead of going by brand … I would focus on talking with some of the better memory foam suppliers that are listed in the topper guidelines I linked earlier and give them as much detail as you can about your criteria so they can help you make the best possible choice out of the toppers they have available and help you compare their memory foam toppers to others that you are considering.
Their return or exchange policies may also be an important consideration if you aren’t confident that a topper you purchase will work well for you.
Phoenix