Hi cschell.
Welcome to our forum :)!
It seems that you got a very good life span out of your previous mattress before it needed to be replaced and given that it worked so well for you it would not be unreasonable to want to replace it with something similar. I am not familiar with a bed from 13 years ago and I would not know if what you are currently considering would be comparable with the previous one. This is a question that you may wish to ask the manufacturer themselves.
Memory foam does a very good job at minimizing motion transfer, but it will generally be the least breathable and most insulating of the foam comfort materials, so temperature can be an issue. If temperature regulation is of concern you’d want to make sure that you don’t choose something with so much memory foam on top that you sink in too deeply. Even the newer generation of more breathable gel memory foams are not as breathable or open celled as other types of foam. Because it absorbs energy, has little resilience and is a poorly supportive material and relies on the layers underneath to provide support and spinal alignment. Even though you are light and petite with thicker layers there is little support for the lumbar area which does not come in firm contact with the support layers and will not be held up well by a foam that “melts” under pressure.
Regarding cooling memory foam claims, you can read more about phase change materials in post #9 here and at the end of post #4 here) and you can read more about the various different types of gel foams in post #2 here. In general terms gel foams will tend to have a temporary effect on temperature while you are first going to sleep until temperatures equalize but have less effect on temperature regulation throughout the course of the night.
Copper itself is a very thermal conductive material so it would make sense that copper fiber infused memory foam (or other types of more advanced thermally conductive materials such as graphite) would be a little more effective than the gel that is more commonly used but it would also depend on the amount of copper that was in the memory foam.
In very general terms … gel and/or other thermal conductive or phase change materials can have “some effect” on the sleeping temperature of a particular material but how much of an effect they will have and how long the effect will last will depend on the specific formulation of the material and on the “combined effect” of all the other materials and components of the sleeping system including your sheets, mattress protector, and bedding. Many thermal conductive or phase change materials tend to have a more temporary effect when you first go to sleep at night or over the first part of the night than they will over the entire course of the night.
As it seems that you would like to replicate the feel of your old mattress, I would suggest that you reach out the manufacturer as they would be the best to best match and provide the appropriate support that would keep you in neutral alignment throughout the night.
Phoenix