As Pamela mentioned, Saltelli's book Global Sensitivity Analysis is one of the best reads out there when it comes to sensitivity analysis. It is the book I used during my thesis.Â
There are many good tools and methods out there, however, make sure the one you choose applies to the type of analysis you want to perform. Keep it as simple as possible at first and gradually increase the level of complexity (including more non-fixed parameters and calculating correlations). I can't stress enough how highly correlated are all the variables in Building Physics and how the transient nature of modeling them makes sensitivity analysis even harder. I found out the hard way (running and hitting a wall several times!).
Good luck, be patient and you'll get there.