By cool I mean not hot. I will be moving to Arizona and I am looking to purchase a memory foam mattress. However I know most memory foam mattresses sleep hot, so I am looking for the coldest one. I am currently considering Purple but I am afraid it would take too long to ship. Any recommendations?
Hi Rouge22,
Welcome to the Mattress Forum! 
Memory foam pourers are constantly attempting to come up with newer versions with more open-cell structure in the memory foam and less of the viscous nature, and some manufacturers changing over to some of the newer high-performance polyfoams that are quite plush but have a more breathable structure than traditional memory foam, but these don’t have the slow-recovery that many people prefer in true memory foam products.
Regarding coolness of 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.
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. 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.
Overall, there is no standardized testing for temperature regulation with different combinations of materials, and 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 and on where you are in the “oven to iceberg” range.
If you’re looking for other online sources for memory foam, you may wish to look at some of the site members listed in post #21 here who are all very experienced and knowledgeable and specialize in providing the type of help and guidance on the phone that can help you make good choices. There are some memory foam options included in the choices there and I believe that all of them compete well with the best in the industry in terms of their quality, value, service, and transparency.
Purple is not a memory foam mattress. It instead uses buckling column gel in the upper layers. You can see more about the specifications of the Purple mattress in the simplified choice thread here. I’m unsure of their current shipping times, but you could phone their customer service to inquire.
Phoenix