Horizontal wavenumber spectra of temperature in the unstably stratified oceanic surface layer were determined from measurements on a bow boom at a depth of 2 m. Spectra were estimated in the wavelength band from 2 m to 2 km and normalized in accordance with Monin-Obukhov similarity theory while accounting for the enhancement of turbulent kinetic energy dissipation due to wave processes. A general form of the temperature spectrum was derived as a function of the stability parameter z/L and wave parameter u*/(gz)^1/2, where z is the depth, L is the Monin-Obukhov length, u* is the friction velocity, and g is the acceleration due to gravity. The wavenumber weighted temperature spectrum has a +1 slope at low wave numbers and a -2/3 slope at high wavenumbers (characteristic of an inertial subrange). The spectral level in the inertial subrange varies with u*/(gz)^1/2, and the spectrum spreads as a function of z/L at low wavenumbers. The wavelength of the spectral peak decreases as z/L decreases, while the magnitude of the peak depends on stability and wave processes. In the absence of waves, the general spectrum spreads at low wavenumbers as a function of z/L. The variation of the spectral level in the inertial subrange with the wave parameter is consistent with enhanced dissipation due to wave processes increasing from a factor of one (no enhancement) at low wind speeds to a factor of three at a wind speed of 10 m/s. The variance of the turbulent temperature fluctuations is proportional to (- z/L )^-1/3 for -z/L > 0.5, consistent with the predictions of similarity theory when wave processes are negligible and consistent with atmospheric surface layer observations. The results of a large eddy simulation turbulence model confirm the behavior of the temperature variance as a function of z/L.