Question: I feel silly asking this but I can’t find the way to create “heat map” style surface representations in ArcMap. Can you help?
Answer: No problem, our profession is riddled with ambiguous terminology (one of the reasons I have a job). The Spatial Analyst has a suite of interpolation tools, and the online help for this area is generally quite good. The intro. help topic is called Understanding interpolation analysis and the related topics will get you to the rest of what you need to know.
From your follow up email, it sounds like you’ve got point data which will be the input to any of the interpolation tools. Read about the various methods and determine which tool is best for your needs. You can either set an analysis mask or use the Raster Clip tool after the fact to trim the edges of your raster output to your geography (if needed–the values outside of your geography will become NO DATA).
From there it is just a matter of choosing a color ramp to represent that values in your raster output. See the Hot Spot Analysis map on mapping center (panel #4) for an example of this process.