The only way I can think of is to put a small logger (file logger would do) using the
error_log php function.
You create a file on your computer (empty text file) and you upload it on your site. You make the file writeable. Then in the showflat and showthreaded files you introduce the logging facility using as the output source the text file you have just uploaded (make sure the path and name of the file passed to the error_log function are correct.
You can collect any number of data and regarding the user that reads that forum. One of them would be their IP address, time etc. A simple if statement can restrict logging only to the board you are interested in.