The detection of Earth-mass exoplanets in the habitable zone around solar-mass stars using the radial velocity technique requires extremely high precision, on the order of 10$,$cm$,$s$^{-1}$, below the intrinsic variability of even relatively inactive stars, such as the Sun. One such variable is convective blueshift varying temporally, spatially, and between spectral lines. We develop a new approach for measuring convective blueshift and determine the strength of convective blueshift for 810 stars observed by the HARPS spectrograph, spanning spectral types late-F, G, K, and early-M. We derive a model for infering blueshift velocity for lines of any depth in later-type stars of any effective temperature. Using a custom list of spectral lines, covering a wide range of absorption depths, we create a model for the line-core shift as a function of line depth, commonly known as the third signature of granulation. We utilize an extremely-high-resolution solar spectrum (R$sim$1$,$000$,$000) to empirically account for the nonlinear nature of the third signature. The solar third signature is then scaled to all 810 stars. Through this we obtain a measure of the convective blueshift relative to the Sun as a function of stellar effective temperature. We confirm the general correlation of increasing convective blueshift with effective temperature and establish a tight, cubic relation between the two that strongly increases for stars above $sim$5800$,$K. For stars between $sim$4100$,$K and $sim$4700$,$K we show, for the first time, a plateau in convective shift and a possible onset of a plateau for stars above 6000$,$K. Stars below $sim$4000$,$K show neither blueshift nor redshift. We provide a table that lists expected blueshift velocities for each spectral subtype in the data set to quickly access the intrinsic noise floor through convective blueshift for the radial velocity technique.
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