MiniProfiler Extensions allows save MiniProfiler results into file (or another source) by log4Net
All what you need is:
var logger = LogManager.GetLogger("Logger"); //Init Log4Net Logger
MiniProfilerLog.SetUpLog4Net(logger); //Set up profiler with logger
and use Profiler as usual (see [MiniProfiler site] (http://miniprofiler.com/) or example Project)
##Install from Nuget
Install-Package MiniProfiler.Log4Net