We identify the fading X-ray afterglow of GRB 001025A from XMM-Newton observations obtained 1.9-2.3 days, 2 years, and 2.5 years after the burst. The non-detection of an optical counterpart to an upper limit of R=25.5, 1.20 days after the burst, makes GRB 001025A a ``dark burst. Based on the X-ray afterglow spectral properties of GRB 001025A, we argue that some bursts appear optically dark because their afterglow is faint and their cooling frequency is close to the X-ray band. This interpretation is applicable to several of the few other dark bursts where the X-ray spectral index has been measured. The X-ray afterglow flux of GRB 001025A is an order of magnitude lower than for typical long-duration gamma-ray bursts. The spectrum of the X-ray afterglow can be fitted with an absorbed synchrotron emission model, an absorbed thermal plasma model, or a combination thereof. For the latter, an extrapolation to optical wavelengths can be reconciled with the R-band upper limit on the afterglow, without invoking any optical circumburst absorption, provided the cooling frequency is close to the X-ray band. Alternatively, if the X-ray afterglow is due to synchrotron emission only, seven magnitudes of extinction in the observed R-band is required to meet the R-band upper limit, making GRB 001025A much more obscured than bursts with detected optical afterglows. Based on the column density of X-ray absorbing circumburst matter, an SMC gas-to-dust ratio is insufficient to produce this amount of extinction. The X-ray tail of the prompt emission enters a steep temporal decay excluding that the tail of the prompt emission is the onset of the afterglow (abridged).
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