  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.
