Photoabsorption spectra of KArn (n = 1-10) are simulated at temperatures ranging between 5 and 25 K. The calculations associate a Monte Carlo (MC) method to sample cluster geometries at temperature T, with a one-electron ab initio model to calculate the ground-state and excited-state energies of the cluster. The latter model replaces the K+ core electrons and all the electrons of the Ar atoms by appropriate pseudopotentials, complemented by core polarization potentials. It also provides the necessary oscillator strengths to simulate the spectra. Global optimization by basin-hopping is used in combination with MC simulation at low temperature (5 K) to identify the most stable isomer and remarkable isomers of ground-state KArn clusters, which are stable with respect to deformations of the order of those expected with Zero Point Energy motions. The absorption spectra calculated for each of these isomers at 5 K suggest that absorption spectroscopy can probe sensitively the local environment of K atom: surface location of K with respect to a close-packed Ar moiety, number of Ar atom in close vicinity, and local symmetry about K. Simulation at increasing temperatures, up to the evaporation limit of K out of the cluster, shows the onset of large amplitude motions above 20 K, when the K atom experiences a variety of local environments.