We present new observations of the [S III] 19 μm, [O III] 52 and 88 μm, and [N III] 57 μm 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 (DG) 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) DG (kpc), [N/H] = (-3.58 +/- 0.04) - (0.072 +/- 0.006) DG (kpc), and [O/H] = (-2.85 +/- 0.06) - (0.064 +/- 0.009) DG (kpc), and we derive Te = (4560 +/- 220) + (390 +/- 40) DG (kpc). The Te gradient is consistent with the Te gradient determined independently via radio recombination lines (Afflerbach et al.). We observe no dependence of S/O, N/O, or Teff on DG. Gradients in N++/O++ and O++/S++ are observed in the sense of increasing ionization with increasing DG. This is entirely consistent with the decreased line blanketing with increasing DG required by the above abundance gradients. All three gradients are best fitted by a linear dependence on DG. 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 Teff is 2000-10,000 K lower than Teff 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 >= 35.1 eV, uncertainties in the luminosity-Teff calibration, and/or ionization of H II regions by multiple stars in some sources.