  Until recently it has been believed that the superconductivity in
Sr$_2$RuO$_4$ is described by p-wave pairing. However, both the recent specific
heat and the magnetic penetration depth measurements on the purest single
crystals of Sr$_2$RuO$_4$ appear to be explained more consistently in terms of
f-wave superconductivity. In order to further this hypothesis, we study
theoretically the thermodynamics and thermal conductivity of f-wave
superconductors in a planar magnetic field. We find the simple expressions for
these quantities when $H \ll H_{c2} $ and $T \ll T_{c}$, which should be
readily accessible experimentally.
