  We calculate the one-loop contributions to the difference \Delta_{\pi K}
between the isoscalar on-shell pion-kaon scattering amplitude at the
Cheng-Dashen point and the scalar form factor \Gamma_K (2M_\pi^2) in the
framework of three flavor chiral perturbation theory. These corrections turn
out to be small. This is further sharpened by treating the kaons as heavy
fields (two flavor chiral perturbation theory). We also analyze the two-loop
corrections to the kaon scalar form factor based on a dispersive technique. We
find that these corrections are smaller than in the comparable case of the
scalar form factor of the pion. This is related to the weaker final state
interactions in the pion-kaon channel.
