For dynamic bioheat transfer problems, this paper proposes a radial basis function pseudo-spectral model with ghost points (RBF-PS-G), which is based on the Runge-Kutta method for time discretization. In contrast to the conventional RBF-PS method, RBF-PS-G extends the center points to envelop a closed region encompassing the problem domain, which boosts the stability of solving the biological heat conduction equation while maintaining efficiency. Furthermore, the impact of shape parameters on the accuracy of RBF-PS is also reduced. Besides, the time evolution is analyzed using the fourth-order Runge-Kutta method. In order to establish the ordinary differential equation, the convection boundary and heat flux conditions conduct Taylor's expansion, which is then assembled into the differential matrix of the governing equation. Through the 2D and 3D numerical simulation of the liver, results demonstrate that the proposed method exhibits enhanced stability over a larger range of R, while improving the accuracy of RBF.