0.935Ba$TiO_3$-0.065($Bi_{0.5}Na_{0.5}$)$TiO_3+xmol%MnO_2$ (BBNTM-x) ceramics with $0{leq}x{leq}0.05$ were fabricated with muffled sintering by a modified synthesis process. Their microstructure and enhanced positive temperature coefficient of resistivity (PTCR) characteristics were systematically investigated in order to obtain lead-free high TC PTCR thermistors. All specimens showed a perovskite structure with a tetragonal symmetry and no secondary phase was observed. Grain growth was achieved when the doped MnO2 was increased above 0.02 mol%. This is due to the effect of positive Mn ion doping as an acceptor compensating a Ba vacancy occurred by the higher donor dopant concentration of $Bi^{3+}$ ion. Especially, enhanced PTCR characteristics of the extremely low ${ ho}_{RT}$ of $9;{Omega}{cdot}cm$, PTCR jump of $5.1{ imes}10^3$, ${alpha}$ of 15.5%/$^{circ}C$ and high $T_C$ of $167^{circ}C$ were achieved for the BBNTM-0.04 ceramics.