We investigate the color SU(3) gauge theory with six-flavors of fermions (Nf = 6)
in the fundamental representation at finite temperature (T) by using the lattice gauge theory.
This work is a part of our project which aims at clarifying the phase diagram of
the chiral phase transition in T-Nf plane and at specifying the conformal window
in this phase diagram.
After the brief review on the recent status of the conformal window, we explain our strategy to attack the conformal window in our finite T treatment, and show some preliminary results.