s23+ and razer cooler

I was wondering if the mag safe phone cooler works for the s23+ because the area that the heat comes from on the phone isn't cooled. I have the universal clamp version of the cooler and due to the phones camera layout it doesn't allow for the cooler to rest flat on the phone. If I move the coolor to the middle of the phone it doesn't allow from proper cooling if any. Especially right now in the summer my phone still gets pretty warm to the point where my phone still gets uncomfortably warm to the touch, and my phones game launcher reads the temp as hot. Please if anyone can answer my questions it would be much appreciated 🙏.