  Here, we study the thermoelectric properties of topological semimetal CoSi in
the temperature range $300-800$ K by using combined experimental and density
functional theory (DFT) based methods. CoSi is synthesized using arc melting
technique and the Rietveld refinement gives the lattice parameters of a = b = c
= 4.445 {\AA}. The measured values of Seebeck coefficient (S) shows the
non-monotonic behaviour in the studied temperature range with the value of
$\sim-$81 $\mu$V/K at room temperature. The $|S|$ first increases till 560 K
($\sim-$93 $\mu$V/K) and then decreases up to 800 K ($\sim-$84 $\mu$V/K)
indicating the dominating n-type behaviour in the full temperature range. The
electrical conductivity, $\sigma$ (thermal conductivity, $\kappa$) shows the
monotonic decreasing (increasing) behaviour with the values of $\sim$5.2$\times
10^{5}$ (12.1 W/m-K) and $\sim$3.6$\times 10^{5}$ (14.2 W/m-K)
$\Omega^{-1}m^{-1}$ at 300 K and 800 K, respectively. The $\kappa$ exhibits the
temperature dependency as, $\kappa \propto T^{0.16}$. The DFT based Boltzmann
transport theory is used to understand these behaviour. The multi-band electron
and hole pockets appear to be mainly responsible for deciding the temperature
dependent transport behaviour. Specifically, the decrease in the $|S|$ above
560 K and change in the slope of $\sigma$ around 450 K are due to the
contribution of thermally generated charge carriers from the hole pockets. The
temperature dependent relaxation time is computed which shows temperature
dependency of $1/T^{0.35}$. Present study suggests that electronic
band-structure obtained from DFT provides reasonably good estimate of the
transport coefficients of CoSi in the high temperature region of $300-800$ K.
