I can't tell you how to do it in ArcGIS, but with QGIS (free) it's pretty easy and straight forward.
Note: Stick with the 2.6.1 version, as 2.8 is still a bit buggy.
As i do not have your data, i downloaded some maritime census data from OBIS.
1) Open QGIS and install the Heatmap and OpenLayers Plugins
2) Import Web>OpenLayers>GMaps>Satellite as a background reference to your project.
3) Import your datatable to your project, define your X/Y columns, create a spatial index and set the CRS (most likely WGS84/EPSG:4326).
Your project should now look smth. like this:
Looks a bit messy with all that points, so we "convert" them to a heatmap
4) Open the Raster>Heatmap>Heatmap dialog, select your point data as "input" and name a path for your output-file.
The most important setting is the
and to an extend rows/columns.
Rows/Columns define the resolution of the output-raster, Radius controlls the smoothing of the hotspots .. this will need some try&error.
Depending on your parameter, the calculation may take some time, but eventually leaves you with something like this:
5) Now we style the output:
double click on the heatmap in your layer-list to open the properties dialog (1)
set the render-type to "pseudocolor" and choose colors of your liking (2)
set the accuracy to "actual" and click "load" to load the values(3)
classify the values(4)
double click on the "0" value and set the opacity to full transparent (5)
Your output will look something like this:
with some other "Radius" setting in #4:
Hope that helps.