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

Palatini $f(R)$ gravity and variants of k-/constant roll/warm inflation within variation of strong coupling scenario