Positive temperature coefficient of resistivity (PTCR) characteristics of (1-x)$BaTiO_3-x(Bi_{0.5}K_{0.5})TiO_3$ ceramics doped with $Nb_2O_5$ were investigated in order to develop the Pb-free PTC thermistor available at high temperatures of > $120^{circ}C$. The PTCR characteristics appearing in the ($B_{i0.5}K_{i0.5})TiO_3$ (< 5 mol%) incorporated $BaTiO_3$ ceramics, which might be mainly due to $Bi^{+3}$ ions substituting for $Ba^{+2}$ sites. The 0.99$BaTiO_3-0.01(Bi_{0.5}K_{0.5})TiO_3$ ceramics showed good PTCR characteristics of a low resistivity at room temperature (${ ho}_r$) of $31{Omega}{cdot}cm$ a high ${ ho}_{max}/{ ho}_{min}$ ratio of $5.38{ imes}10^3$, and a high resistivity temperature factor (${alpha}$) of $17.8%/^{circ}C$. The addition of $Nb_2O_5$ to 0.99$BaTiO_3-0.01(Bi_{0.5}K_{0.5})TiO_3$ ceramics further improved the PTCR characteristics. Especially, 0.025 mol% $Nb_2O_5$ doped 0.99$BaTiO_3-0.01(Bi_{0.5}K_{0.5})TiO_3$ ceramics exhibited a significantly increased ${ ho}_{max}/{ ho}_{min}$ ratio of $8.7{ imes}10^3$ and a high ${alpha}$ of $18.6%/^{circ}C$, along with a high $T_c$ of $148^{circ}C$ despite a slightly increased ${ ho}_r$ of $31{Omega}{cdot}cm$.