The absolute brightness temperature of the Sun at millimeter wavelengths is an important diagnostic of the solar chromosphere. Because the Sun is so bright, measurement of this property usually involves the operation of telescopes under extreme conditions and requires a rigorous performance assessment of the telescope. In this study, we establish solar observation and calibration techniques at 2.6-mm wavelength for the Nobeyama 45-m telescope and derive the absolute solar brightness temperature accurately. We tune the superconductor-insulator-superconductor (SIS) receiver by inducing different bias voltages onto the SIS mixer to prevent saturation. Then, we examine the linearity of the receiver system by comparing outputs derived from different tuning conditions. Further, we measure the lunar filled beam efficiency of the telescope using the New Moon, and then derive the absolute brightness temperature of the Sun. The derived solar brightness temperature is 7700+-310 K at 115 GHz. The telescope beam pattern is modeled as a summation of three Gaussian functions and derived using the solar limb. The real shape of the Sun is determined via deconvolution of the beam pattern from the observed map. Such well-calibrated single-dish observations are important for high-resolution chromospheric studies because they provide the absolute temperature scale missing from interferometer observations. ; Comment: 27 pages, 6 figures, accepted in publication of Solar Physics