  Based on the feature of chiral susceptibility and thermal susceptibility at
finite temperature, the nature of chiral phase transition around the critical
number of fermion flavors ($N_c$) and the critical temperature ($T_c$) at a
fixed fermion flavors number in massless QED$_3$ are investigated. It is showed
that, at finite temperature the system exhibits a second-order phase transition
at $N_c$ or $T_c$ and each of the estimated critical exponents is less than 1,
while it reveals a higher-order continuous phase transition around $N_c$ at
zero temperature.
