Hi rupekate,
Welcome to the Mattress Forum! 
I’m sorry your husband is sleeping too warm on your new mattress. Unfortunately, it’s not really possible to quantify the sleeping temperature of a mattress for any particular person with any real accuracy because there are so many variables involved including the type of mattress protector and the sheets and bedding that you use (which in many cases can have just as significant an effect on sleeping temperature as the type of foam in a mattress) and on where you are in the “oven to iceberg” range and because there is no standardized testing for temperature regulation with different combinations of materials.
There is much more complete information about the many variables that can affect the sleeping temperature of a mattress or sleeping system in post #2 here that can help you choose the types of materials and components that are most likely to keep you in a comfortable temperature range.
In very general terms … 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 or foam toppers will tend to be more “insulating” and for some people can sleep warmer than firmer versions of the same material.
You weren’t very specific about your current mattress, other than it uses “natural fibres”, but a mattress that is softer, or one that you sink into a bit more, can sleep warmer, as it will be more insulating than a mattress that is firmer and you sleep more “upon”. Many natural fibres can be quite breathable and be good at both temperature and moisture regulation (such as wool), but this would depend upon the amount and location within a mattress or mattress pad. As for foams, latex (specifically Talalay latex) will be your most breathable, followed by polyfoam and then memory foam.
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.
I hope that helps get you started on evaluating your current configuration.
Phoenix