Would like to create a heat map in ArcMap based only on values of points rather than density.
For example lets say two points have value 10 and are 1 mile apart. And there's a third point 20 miles away with value of 10 as well. In this case the heat would be equal across the entire region of interest rather than hotter near the two near points.
The point density tool utilising a population field would kind-of replicate what you intend, but not really.
From what you're saying, a kernel density would not be appropriate as it would diminish over distance.
for any large number of points this would probably become intractable. i.e. what about points 21 miles the opposite direction to the point 20 miles way? What about points 10 miles from the other point?
My best advice would be to choose the maximum distance you wish points to have an effect on the surface (e.g. 20 miles cutoff), use that as the search radius and use the population value from your intensity field.