Hi Jacqulyn.
Welcome to our Mattress Forum! 
Good to hear that although you have some temperature issues, the Urban Green Mattress meets your comfort and support needs. It is very likely that with a bit of detective work you’ll be able to track down the contributing factors and adjust your sleeping microclimate.
All foams are insulators (rather than heat conductors) so to some degree they will all be warmer than mattresses that contain no foam at all (such as mattresses that only have an innerspring and layers of natural fibers on top) but these tend to be premium or super premium mattresses and for the most part almost all mattresses have some type of foam in the comfort layers.
It is important to recognize that no two people are alike, and even with naturally derived materials such as latex that is known to be the most breathable and “temperature neutral” relative to all the different types of foam materials, how it feels to a particular individual is very personal and usually is the result of many interconnected variables including room temperature, humidity, sheets, bedding, and bedclothes, mattress protector or any mattress pads or toppers being used, and of course where you are in the “oven to iceberg” range. The firmness of the mattress and how much you sink into the mattress is also an important factor that can affect the sleeping temperature in addition to the fact that some people can sleep warmer on mattresses that most people are generally fine with.
There is more about tracking down a potential cause or causes for temperature regulation issues (at least to the degree possible for a specific mattress) in post #2 here.and the posts it links to that may be helpful, but generally speaking 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.
A mattress breaths from all sides to different degrees and placing your mattress upon plywood would prevent the mattress ventilating from underneath which may be a large contributor to the heat buildup you are experiencing. You may wish to consider something like a coir bed rug under the mattress. or placing your mattress on firm breathable slated base that allows for sufficient air flow.
The waterproof mattress pad/protector you are using may have a significant effect on the temperature regulation because it can add to the insulating effect or to the moisture wicking effect of your mattress. You can see more about the effect of different mattress protectors in post #89 here.
The best way to track down where temperature issues are coming from would be to look at all the layers between your skin and the floor to see if any of them could be contributing to the temperature issue. Layers or materials that are closer to you and are more breathable and allow for more moisture wicking will help with temperature regulation issues while layers that allow for less airflow or moisture wicking that are closer to you can make them worse.
Your sheets are cotton so this shouldn’t be an issue and a 300 thread count would not be high enough to trap the heat. Linen sheets are probably the coolest sleeping type of fabric but they can also be costly. There is more about how different types of mattress protectors can affect sleeping temperature in post #89 here . Finally the next layers down would normally be the mattress itself which includes the cover and the top layers of foam.
Your blankets and bedding and the temperature or humidity of the room can also make a difference if there are no layers underneath you that can be changed that are part of the underlying cause of the temperature issue.
Wool is among the best temperature regulating material but I would also keep in mind that it regulates temperature in both directions (it’s used in the desert and also in cold climates because of this) so while it may not feel “cool” … it generally doesn’t feel “hot” either and it also helps to regulate moisture (which can trap heat) and reduce the perception of temperature that comes from higher humidity levels (similar to how temperatures feel cooler on less humid days than they do on more humid days).
In many cases changing the mattress protector, sheets, or bedding to cooler versions can make “enough” of a difference for many people who would otherwise sleep hot on a mattress. It would also be worth mentioning that your face and head is also a major part of how your body regulates temperature and a cooler pillow can sometimes make a surprising difference in how warm you sleep as well. Temperature issues are usually a combination of factors and can be a bit complex, but with a bit of experimenting and adjusting your sleeping microclimate, you’ll be able to get the cool and quality sleep and rest you are looking for.
I’ll be interested to learn about how you progress through your evaluation and any changes that you are able to make.
Phoenix