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We present a sample-variance-limited measurement of the temperature powerspectrum ($TT$) of the cosmic microwave background (CMB) using observations ofa $\sim\! 1500 \,\mathrm{deg}^2$ field made by SPT-3G in 2018. We reportmultifrequency power spectrum measurements at 95, 150, and 220GHz covering theangular multipole range $750 \leq \ell < 3000$. We combine this $TT$measurement with the published polarization power spectrum measurements fromthe 2018 observing season and update their associated covariance matrix tocomplete the SPT-3G 2018 $TT/TE/EE$ data set. This is the first analysis topresent cosmological constraints from SPT $TT$, $TE$, and $EE$ power spectrummeasurements jointly. We blind the cosmological results and subject the dataset to a series of consistency tests at the power spectrum and parameter level.We find excellent agreement between frequencies and spectrum types and ourresults are robust to the modeling of astrophysical foregrounds. We reportresults for $\Lambda$CDM and a series of extensions, drawing on the followingparameters: the amplitude of the gravitational lensing effect on primary powerspectra $A_\mathrm{L}$, the effective number of neutrino species$N_{\mathrm{eff}}$, the primordial helium abundance $Y_{\mathrm{P}}$, and thebaryon clumping factor due to primordial magnetic fields $b$. We find that theSPT-3G 2018 $T/TE/EE$ data are well fit by $\Lambda$CDM with aprobability-to-exceed of $15\%$. For $\Lambda$CDM, we constrain the expansionrate today to $H_0 = 68.3 \pm 1.5\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$ and thecombined structure growth parameter to $S_8 = 0.797 \pm 0.042$. The SPT-basedresults are effectively independent of Planck, and the cosmological parameterconstraints from either data set are within $<1\,\sigma$ of each other.(abridged)

A Measurement of the CMB Temperature Power Spectrum and Constraints on Cosmology from the SPT-3G 2018 TT/TE/EE Data Set