The first results under fired internal combustion engine conditions based on a supercontinuum absorption spectrometer are presented and discussed. Temperature, pressure, and water mole fraction are inferred simultaneously from broadband H_2O absorbance spectra ranging from 1340 nm to 1440 nm. The auto-ignition combustion process is monitored for two premixed n-heptane/air mixtures with 10 kHz in a rapid compression machine. Pressure and temperature levels during combustion exceed 65 bar and 1900 K, respectively. To allow for combustion measurements, the robustness of the spectrometer against beam steering has been improved compared to its previous version. Additionally, the detectable wavelength range has been extended further into the infrared region to allow for the acquisition of distinct high-temperature water transitions located in the P-branch above 1410 nm. Based on a theoretical study, line-of-sight (LOS) effects introduced by temperature stratification on the broadband fitting algorithm in the complete range from 1340 nm to 1440 nm are discussed. In this context, the recorded spectra during combustion were evaluated only within a narrower spectral region exhibiting almost no interference from low-temperature molecules (here, P-branch from 1410 nm to 1440 nm). It is shown that this strategy mitigates almost all of the LOS effects introduced by cold molecules and the evaluation of the spectrum in the entirely recorded wavelength range at engine combustion conditions.