We study both the temperature and band-gap dependence of the first-and third-order intraband conductivities of a Weyl semimetal (WSM) as well as the resultant critical field. By a semiclassical model we further explore how different chemical potentials, cone separations, field geometries, and finite relaxation times affect photoresponse. We determine that the band-gap variation is characterized by the Weyl cone separation and observe significant thermal enhancement of the nonlinear response. Universal behaviors of both the linear and nonlinear response have also been observed under certain conditions. Coupled with experimentally accessible critical field values of 104-105 V m-1, our results give strong impetus for the use of WSMs as tunable photo-mixers.