  The transverse momentum (pt) dependence, the centrality dependence and the
rapidity dependence of the elliptic flow of thermal photons in Au+Au collisions
at $\sqrt{s_{NN}}=200$ GeV are predicted, based on a three-dimensional ideal
hydrodynamic description of the hot and dense matter. The elliptic flow
parameter $v_{2}$, i.e. the second Fourier coefficient of azimuthal
distribution, of thermal photons, first increases with $\pt$ and then decreases
for $\pt>$ 2 GeV/$c$, due to the weak transverse flow at the early stage. The
$\pt$-integrated $v_{2}$ first increases with centrality, reaches a maximum at
about 50% centrality, and decreases. The rapidity dependence of the elliptic
flow $v_{2}(y)$ of direct photons (mainly thermal photons) is very sensitive to
the initial energy density distribution along longitudinal direction, which
provides a useful tool to extract the realistic initial condition from
measurements.
