Specific heat measurements have been made in K0.3MoO3 and Tl0.3MoO3 using an adiabatic continuous heating method from 100 K to 220 K. It is found that Peierl transitions occur at 177.5 K and 172.3 K for K0.3MoO3 and Tl0.3MoO3 respectively. Analyses of specific heat data near Peierls transitions yield that widths of critical regions are about 6 K and 8 K for K0.3MoO3 and Ti0.3MoO3 respectively and the critical behavior belongs to the three dimensional XY model.