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We will show results for the Holstein polaron spectral function on a one dimensional ring computed by using the finite–temperature (T) Lanczos method. With increasing T additional features in the spectral function emerge already at temperatures below the phonon frequency. We observe a substantial spread of the spectral weight towards lower frequencies and the broadening of the quasiparticle (QP) peak. In the weak coupling regime the QP peak merges with the continuum in the high-T limit. In the strong coupling regime the main features of the low–T spectral function remain detectable up to the highest T used in our calculations. The effective polaron mass shows a non–monotonous behavior as a function of T at small phonon frequency but increases with T at larger frequencies. The self energy remains k-independent even at elevated T in the frequency range corresponding to the polaron band.