Context. The temporal and spatial spectral evolution of the jets of Active Galactic Nuclei (AGN) can be studied with multi-frequency, multi-epoch very-long-baseline-interferometry (VLBI) observations. The combination of both, morphological (kinematical) and spectral parameters can be used to derive source intrinsic physical properties such as the magnetic field and the non-thermal particle density. Such a study is of special interest during the high states of activity in AGNs since VLBI observations can provide estimates on the location of the flaring site. Furthermore, we can trace the temporal variations of the source intrinsic parameters during the flare, which may reflect the interaction between the underlying plasma and a traveling shock wave. The source CTA102 exhibited such a radio flare around 2006 Aims. In the first two papers of this series (Papers I & II) we analyzed the single-dish light curves and the VLBI kinematics of the blazar CTA102 and suggested a shock-shock interaction between a traveling and a standing shock wave as a possible scenario to explain the observed evolution of the component associated to the 2006 flare. In this paper we investigate the core-shift and spectral evolution to test our hypothesis of a shock-shock interaction. Methods. We used eight multi-frequency Very Long Baseline Array (VLBA) observations to analyze the temporal and spatial evolution of the spectral parameters during the flare. We observed CTA102 between May 2005 and April 2007 using the VLBA at six different frequencies spanning from 2GHz up to 86GHz. After the calibrated VLBA images were corrected for opacity, we performed a detailed spectral analysis. We developed methods for the alignment of the images and extraction of the uncertainties in the spectral parameters. From the derived values we estimated the magnetic field and the density of the relativistic particles and combined those values with the kinematical changes provided from the long-term VLBA monitoring (Paper II) and single-dish measurements (Paper I). Results. The detailed analysis of the opacity shift reveals that the position of the jet core is proportional to ν^−1 with some temporal variations. The value suggests possible equipartition between magnetic field energy and particle kinetic energy densities at the most compact regions. From the variation of the physical parameters we deduced that the 2006 flare in CTA102 is connected to the ejection of a new traveling feature (tej = 2005.9) and the interaction between this shock wave and a stationary structure (interpreted as a recollimation shock) around 0.1mas from the core (de-projected 18 pc at a viewing angle of ϑ = 2.6◦). The source kinematics together with the spectral and structural variations can be described by helical motions in an over-pressured jet.