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Here we explore the role of temporal fluctuations in kinetic helicity on thegeneration of large-scale magnetic fields in presence of a background linearshear flow. Key techniques involved here are same as in our earlier work\citep[][hereafter paper~I]{JS20}, where we have used the renovating flow basedmodel with shearing waves. Both, the velocity and the helicity fields, aretreated as stochastic variables with finite correlation times, $\tau$ and$\tau_h$, respectively. Growing solutions are obtained when $\tau_h > \tau$,even when this time-scale separation, characterised by $m=\tau_h/\tau$, remainsbelow the threshold for causing the turbulent diffusion to turn negative. Inregimes when turbulent diffusion remains positive, and $\tau$ is on the orderof eddy turnover time $T$, the axisymmetric modes display non-monotonicbehaviour with shear rate $S$: both, the growth rate $\gamma$ and thewavenumber $k_\ast$ corresponding to the fastest growing mode, first increase,reach a maximum and then decrease with $|S|$, with $k_\ast$ being alwayssmaller than eddy-wavenumber, thus boosting growth of magnetic fields at largelength scales. The cycle period $P_{\rm cyc}$ of growing dynamo wave isinversely proportional to $|S|$ at small shear, exactly as in the fixed kinetichelicity case of paper~I. This dependence becomes shallower at larger shear.Interestingly enough, various curves corresponding to different choices of $m$collapse on top of each other in a plot of $m P_{\rm cyc}$ with $|S|$.

Mean field dynamo action in shearing flows. II: fluctuating kinetic helicity with zero mean