Before realizing any device's actual application, it is necessary to understand the materials’s performance through first-principles investigations. Most of the devices consist of nanomaterials, especially thin film-based ones, which are under strain due to a lattice mismatch between the thin film of active material and the substrate on which the thin film is grown. This strain affects the material's properties and overall device performance. In this work, we comprehensively explored strain engineering's impact on the electronic and thermal transport characteristics of the CoHfSi half-Heusler alloy. Employing the self-consistent ultra-soft pseudo-potential method and generalized gradient approximation within a density functional framework, we investigated the effect of both isotropic- and tetragonal-type strains applied at compressive and tensile categories. A semiconducting ground state with an indirect band gap of 1.248 eV is found under 5% compressive isotropic strain, which reduces to 0.847 eV for 5% tensile strain under the same type. On the other hand, the semiconducting energy bandgap increases from 0.986 eV (for 5% compressive) to 1.217 eV (for 5% tensile) for tetragonal strain. The power factor increases with the increase in temperature. It obtains a maximum value of 2.4 ╳1012 Wm-1K-1s-1 for -5% isotropic and +5% tetragonal strain, and around this doping level, a better TE efficiency can be achieved. A maximum and saturated value of zT at 300 K and beyond is estimated to be more than 3.5 and 3 for -2% and -1% isotropic strain, respectively. For +5% isotropic strain, the electronic fitness function attains a maximum ~ 9 ×10-20 W5/3ms-1/3K-2 at 800 K, irrespective of strain type. All these results provide novel insights into the strain-induced effects on the electronic and thermoelectric properties of mechanically and thermodynamically stable CoHfSi at elevated temperatures. Apart from strain-induced modifications, optimum p-type doping can also increase the power factor, figure-of-merit, and electronic fitness function of these strained CoHfSi half-Heusler alloys, demonstrating them as a suitable and promising candidate for thermoelectric applications.