Sheng,
I'll start with your last question first, a Fresnel lens is feasible if the material that the lens is made out of transmits IR in the 4-8 micron wavelengths. See this thread for in-depth discussion of lens materials: http://e2e.ti.com/support/other_analog/temperature_sensors/f/243/t/117229.aspx Polypropylene is the most commonly recommended material as it offers a good compromise between price and transmission performance. An additional consideration is that the TMP006 must be placed at the focal point of the lens, as is true for all lenses. Either improper positioning or the transmission characteristics of the lens material could be responsible for the reduced object temperature that you experienced.
The S0 calculation spreadsheet that Ian posted to your other thread is really the best method to perform the calculation. Because it takes your measurement several minutes to reach a stable state, that indicates that you are measuring something being heated by the water instead of the water itself. Remember that any barrier between the TMP006 and the measurement object must be transparent to IR energy, in this case is the cup transparent to IR?