Using ArcMap's Kernel Density yields this result when applied with defaults to a Toronto schools point layer.
ArcMap has a similar feature with the Point Density tool. Information about both tools can be found here: http://pro.arcgis.com/en/pro-app/tool-reference/spatial-analyst/how-kernel-density-works.htm and
QGIS also has a HeatMap plugin. Information about it can be found here: http://docs.qgis.org/1.8/en/docs/user_manual/plugins/plugins_heatmap.html