We numerically investigated the diffusion of an active Janus particle in periodic arrays of planar counter-rotating convection rolls at high Péclet numbers. We considered convection patterns with distinct longitudinal and transverse advection properties and characterized the dependence of the relevant diffusion constants on the particle's dynamical parameters, namely, self-propulsion speed, correlation time and chirality. Numerical results are interpreted analytically based on qualitative arguments of classical transport theory. The purpose of the present analysis is controlling active matter transport in microfluidic devices.