My shared hosting provider set up IIS recycle app pool every 3 minutes for idle. So my session factory often recreates (at application startup). As I have about 70-100 entities it takes about 2-5 seconds to construct factory. So cold start of my application is rather long. I haven't access to IIS setting.
Have you tried to stop your site from being idle in the first place? I use uptime robot that is FREE and pings your site every 5 minutes. The benefit of this service is that it only requests the headers of the page you set up as a monitor and therefore does not affect logging such as Google Analytics.
However said you will need to test this to see when your app does indeed recycle to see if uptime robot works with your shared hosting provider. The best way is to log every time the session factory is re-built.