In this work, we study warm inflationary scenario based on a deformation of $R^2$ gravity. We start considering $R^p$ and assume $p=2(1+\delta )$ with $\delta \ll 1$ so that we simply obtain warm $R^2$ inflation when setting $\delta =0$. We then derive the potential in the Einstein frame and consider a dissipation parameter of the form $\Gamma =C_{1}T$ with $C_1$ being a coupling parameter. We focus only on the strong regime of which the interaction between inflaton and radiation fluid has been taken into account. We also consider a detailed analysis of the background dynamics, considering the evolution of the relevant quantities. We compute inflationary observables and constrain the parameters of our model using latest observational data reported by Planck. From our analysis, we discover that with proper choices of parameters the derived $n_s$ and r are in good agreement with the Planck 2018 observational constraints. Particularly, we constrain the potential scale $U_0$ of the models.