Hi aneto,
Welcome to the Mattress Forum! 
I’m sorry to learn that you’re having a problem with your second Saatva mattress, but it’s good to know that you had the foresight to choose a mattress that you’re able to return.
Quite often a “lumbar support layer” is simply a piece of foam in the middle third of a mattress. Obviously this is not targeted directly at the lumbar region, which is only five vertebrae, and is also in a slightly different location for individuals of various sizes. More appropriately, these should be termed “middle-third layers”. Their primary task would be to provide a bit more foam in the area of the mattress that gets the most use, hopefully enhancing overall durability.
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.
The materials, layers, and components of a sleeping system that are closer to your skin will have a bigger effect on airflow, moisture transport, and temperature regulation than materials, layers, and components that are further away from your skin, and softer mattresses, memory foams or foam toppers will tend to be more “insulating” and for some people can sleep warmer than firmer versions of the same material.
Phoenix