  We solve a popular effective Hamiltonian of competing $d$-density wave and
d-wave superconductivity orders self-consistently at the mean-field level for a
wide range of doping and temperature. The theory predicts a temperature
dependence of the $d$-density wave order parameter seemingly inconsistent with
the neutron scattering and $\mu$SR experiments of the cuprates. We further
calculate thermodynamic quantities, such as chemical potential, entropy and
specific heat. Their distinct features can be used to test the existence of the
$d$-density wave order in cuprates.
