It may be worth checking your radiator. They can look OK then the fins turn to dust when you touch them, so their heat exchange affect could be reduced quite a bit.
Without a cowl your fan is only going to draw air over the area your fan covers so reducing the area of your radiator that gets sir drawn over it. I presume if you are on a beach you are not moving very fast so the air passing over the rad is only where your fan is where normally the vehicle moving would provide some flow.
As has been said above, moving on sand will take more effort from the engine than normal driving.
I am no expert, so please don't take my comments as an expert opinion, but I have had two land rovers where the rad looked OK only for them to turn to dust when I touched then - one resulting in a cooked V8!