Hi Chrissy500,
Welcome to the Mattress Forum! 
That can be a bit of a complex issue when you are attempting to find one mattress for people with varying needs.
Regarding sleeping positions, there is more information in mattress firmness/comfort levels in post #2 here that speaks to that issue. Side sleepers generally require a bit more surface comfort, back sleepers can generally tolerate a wider range of comfort, and stomach sleepers generally need something that is a bit firmer on top that doesn’t allow your low back to sink in too deeply. All sleeping postures need a product using good and strong deep support that helps to promote a more neutral alignment.
As for different somatotypes, BMIs and sleeping styles, post #2 here goes into quite a bit of detail with options that you may wish to consider. The most common method of accommodation for this would be a side to side split configuration, where each side of the king mattress is configured to the needs of each person within the same king mattress encasement. Another option in a king situation would be two twin extra long mattresses placed next to each other, which would equal a king size. This tends to be used when there are more extreme differences in comfort preference.
Subject to first confirming that any retailer or manufacturer on the list that you wish to visit is completely transparent ( see this article ) and to making sure that any mattress you are considering meets the quality/value guidelines here … some options or possibilities I’m aware of in and around Toronto are listed here.
I do think highly of Novosbed, and they are a site member here. Memory foam, even that with phase change materials or gels added to it, will tend to be less breathable than polyfoam or latex, and it can “feel warmer” to those who are more temperature sensitive. All foams are insulators to a degree, and a mattress that is softer that you sleep “in” more than “on” can also tend to feel warmer for individuals, allowing for less surface are being exposed for heat exchange and more insulation.
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.
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. There is more 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.
Phoenix