QUESTION
How secure are chart images from random viewing?
ANSWER
Every time a chart image is created, its file name is randomly generated in the format of dnc-(random characters).extension such as "dnc-e0cpm16v.png". The images are then cleared from the hard drive based on a time interval specified through the Chart.CleanPeriod property. It is possible but unlikely that someone could guess a filename of a chart file created in the temp directory and view it.
You are also free to set the chart filename directly if you wish to have a specific filename and not depend on the randomly generated filenames. Of course, all generated files are still subject to the security settings from the web server so if you have restricted access to the generated files through NTFS file level permissions only those users explicity granted access would be able to view the generated images.
Finally, you can directly stream images to the browser in which case no file is saved to disk. Please see the sample streamingusage.aspx and streaming.aspx which it consumes for more details.