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(Abridged) We use high S/N spectra of 20 HII regions in the giant spiralgalaxy M101 to derive electron temperatures for the HII regions and robustmetal abundances over radii R = 0.19-1.25 Ro (6-41 kpc). We compare theconsistency of electron temperatures measured from the [O III]4363, [N II]5755,[S III]6312, and [O II]7325 auroral lines. Temperatures from [O III], [S III],and [N II] are correlated with relative offsets that are consistent withexpectations from nebular photoionization models. However, the temperaturesderived from the [O II]7325 line show a large scatter and are nearlyuncorrelated with temperatures derived from other ions. Our derived oxygenabundances O/H are well fitted by an exponential distribution over six diskscale lengths, from approximately 1.3 solar in the center to 1/15 solar in theoutermost region studied (for solar 12 + log (O/H)=8.7). We measure significantradial gradients in N/O and He/H abundance ratios, but relatively constant S/Oand Ar/O. Our abundances are systematically lower by 0.2-0.5 dex than thosederived from the most widely used strong-line "empirical" abundance indicators.We suspect that most of the disagreement with the strong-line abundances arisesfrom uncertainties in the nebular models that are used to calibrate the"empirical" scale, and that strong-line abundances derived for HII regions andemission-line galaxies are as much as a factor of two higher than the actualoxygen abundances. However other explanations, such as the effects oftemperature fluctuations on the auroral line based abundances cannot becompletely ruled out. These results point to the need for direct abundancedeterminations of a larger sample of extragalactic HII regions, especially forobjects more metal-rich than solar.Comment: 50 pages, 14 figures, 8 tables. Accepted by Ap

The Composition Gradient in M101 Revisited. II. Electron Temperatures and Implications for the Nebular Abundance Scale