  We investigate a heating phenomenon in periodically driven integrable systems
that can be mapped to free-fermion models. We find that heating to the
high-temperature state, which is a typical scenario in non-integrable systems,
can also appear in integrable time-periodic systems; the amount of energy
absorption rises drastically near a frequency threshold where the
Floquet-Magnus expansion diverges. As the driving period increases, we also
observe that the effective temperatures of the generalized Gibbs ensemble for
conserved quantities go to infinity. By the use of the scaling analysis, we
reveal that in the limit of infinite system size and driving period, the steady
state after a long time is equivalent to the infinite-temperature state. We
obtain the asymptotic behavior $L^{-1}$ and $T^{-2}$ as to how the steady state
approaches the infinite-temperature state as the system size $L$ and the
driving period $T$ increase.
