Going back to my original question, I can produce the results I want by the methods you are describing for a single day (shapefile) as input. I do not know how to accomplish this in an iterative fashion for many different input shapefiles. The input I am referring to here is the data being interpolated, since the points where I want the predictions will remain constant through the iterative process. I have so many input files that creating a template and using it manually for each one is not feasible, which made me think I should be using the Model Builder or Python, but I cannot get that to work.