Maybe this site will help you: http://www.math.uni-trier.de/~sachs/scientific_interests/projects/mc_calibration.htm (resp. http://link.springer.com/article/10.1007%2Fs00780-009-0097-9)
The testcase (100 plain vanilla option on the S&P 500) for the Heston Model is from the paper by Andersen and...
derivatives of the call are not only taken with respect to strike K but also with respect to maturity T in place of price S and time t. This is made by an adjoint/backward argument. Maybe this paper by Jim Gatheral will help you (especially section 2.2).
Daniel Duffy's "Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach" is quite good!
"Pricing Financial Instruments: The Finite Difference Method" by Tavella and Randall is a good book for FDM as well.