  We calculate the triangular flow parameter $v_3$ of thermal photons from an
event-by-event ideal hydrodynamic model for $0--40\%$ central collisions of Pb
nuclei at $\sqrt{s_{NN}}$=2.76 TeV at LHC. $v_3$ determined with respect to the
participant plane (PP) is found to be non-zero, positive and its $p_T$
dependence is qualitatively similar to the elliptic flow parameter $v_2$(PP) of
thermal photons in the range $1 \le p_T \le 6$ GeV/$c$. In the range $p_T \,
\le $ 3 GeV/$c$, $v_3$(PP) is found to be about $50--75\%$ of $v_2$(PP) and for
$p_T \, >$ 3 GeV/$c$ the two anisotropy parameters become comparable. The local
fluctuations in the initial density distribution as well as the initial global
geometry of the produced matter in the event-by-event hydrodynamic framework
are responsible for this substantial value of $v_3({\rm PP})$. However, as
expected, the triangular flow parameter calculated with respect to the reaction
plane $v_3$(RP) is found to be close to zero. We show that $v_3$(PP) strongly
depends on the value of the fluctuation size scale $\sigma$ especially in the
higher $p_T \, (\ge 3 {\rm GeV}/c)$ region where a larger value of $\sigma$
results in a smaller $v_3({\rm PP})$. In addition, the $v_3{\rm (PP)}$ is found
to increase with the assumed formation time of the thermalized system.
