We present new observations of the [S III] 19 mu m, [O III] 52 and 88 mu m, and [N III] 57 mu m lines toward 18 compact and ultracompact (UC) H II regions. These data were combined with data from the literature and high-resolution radio continuum maps to construct detailed statistical equilibrium and ionization equilibrium models of 34 compact H II regions located at galactocentric distances (D-G) 0-12 kpc. Our models simultaneously fitted the observed IR fine-structure lines and high-resolution radio continuum maps. Abundance gradients are found of the form [S/H] = (-4.45 +/- 0.04) - (0.063 +/- 0.006) D-G (kpc), [N/H] = (- 3.58 +/- 0.04) - (0.072 +/- 0.006) D-G (kpc), and [O/H] = (-2.85 +/- 0.06) - (0.064 +/- 0.009) D-G (kpc), and we derive T-e = (4560 +/- 220) + (390 +/- 40) D-G (kpc). The T-e gradient is consistent with the T-e gradient determined independently via radio recombination lines (Afflerbach el at). We observe no dependence of S/O, N/O, or T-eff on D-G. Gradients in N++/O++ and O++/S++ fare observed in the sense of increasing ionization with increasing D-G. This is entirely consistent with the decreased line blanketing with increasing D-G required by the above abundance gradients. All three gradients are best fitted by a linear dependence on D-G. The abundances are consistent with production of sulfur, nitrogen, and oxygen by primary nucleosynthesis. Comparison with abundances in other galaxies implies a Hubble type between Sab and Sb for our Galaxy and an unbarred or mixed galactic structure (Vila-Costas & Edmunds). Our derived T-eff is 2000-10,000 K lower than T-eff expected from ZAMS stars of the same Lyman continuum flux (Panagia; Vacca et al.), probably owing to uncertainties in the UV flux of stellar models for E greater than or equal to 35.1 eV, uncertainties in the luminnosty-T-eff calibration, and/or ionization of H II regions by multiple stars in some sources.