Extending the transfer-matrix density-matrix renormalization-group algorithm, we are able to calculate imaginary time spin autocorrelations with high accuracy (absolute error textless10-6) over a wide temperature range (0textlessβJtextless20). After analytic continuation using the rules of probability theory along with the entropic prior (MaxEnt), we obtain real frequency spectra for the XY model, the isotropic Heisenberg, and the gapped Heisenberg-Ising model. Available exact results in some limits allow for a critical evaluation of the quality of answers expected from this procedure. We find that high-precision data are still insufficient for resolving specific line shapes such as low-frequency divergences. However, the method is appropriate for identifying low-temperature gaps and peak positions.