Hi Miko,
I have no direct experience with Murphy beds so I would not be the best source of advice.
In cases like this … my “best advice” is to encourage you to talk with several people who are more knowledgeable about Murphy beds which are usually the manufacturers who make them and talk to them about the specifics of your situation. While many mattress manufacturers would have some experience with Murphy beds … all Murphy bed manufacturers would have a great deal of experience with how different mattresses perform on their beds. This is what I did in post #64 here as an example because in areas where I have little specific knowledge I always talk to people who are more knowledgeable than I am.
You will find some conflicting advice and opinions even when you talk with “experts” who have different experiences but when you do this you will also find some consistent “themes” which will help you make more informed “best judgement” decisions.
Logic says to me that an innerspring mattress is stiffer and less floppy than a mattress that has a foam core and would probably do better on a Murphy bed than a more “floppy” mattress.
I can see from your comments that you’ve probably read this but for the benefit of others that read this post #2 here talks in more detail about the many interacting factors that in combination can affect the sleeping temperature of a mattress for those who are looking to “cool down” their mattress.
Phoenix