  We develop the formalism for computing the oscillations of the specific heat
and thermal transport under rotated magnetic field in multiband superconductors
with anisotropic gap and apply it to iron-pnictides. We show that these
oscillations change sign at low temperatures and fields, which strongly
influences the conclusions about the gap structure based on experiment. We find
that recent measurements of the specific heat oscillations indicate that the
iron-based superconductors possess an anisotropic gap with deep minima or nodes
close to the line connecting electron and hole pockets. We make predictions for
the behavior of the thermal conductivity that will help distinguish between
these cases.
