  We show that upon applying Palatini $f(R)$, characterized by an $\a
R^2$-term, within a scenario motivated by a temporal variation of strong
coupling constant, then one gets a quadratic kinetic energy. We do not drop
this term, but rather study two extreme cases: $\a <<1$ and $\a >>1$. In both
cases one can generate a kinematically-induced inflationary paradigm. In order
to fit the Planck 2018 data, the $\a >>1$ case, called k-inflation, requires a
fine tuning adjustment with non-vanishing non-minimal coupling to gravity
parameter $\xi$, whereas the $\a <<1$ case, studied in the constant-roll
regime, can fit the data for vanishing $\xi$. The varying strong coupling
inflation scenario remains viable when implemented through a warm inflation
scenario with or without $f(R)$ gravity.
