The development and verification of a one-dimensional constant density material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method (with an analytical Jacobian) for the entire system of residual equations have been implemented and verified for variable material properties, Q ablation, and thermochemical ablation problems. Timing studies were performed, and when accuracy is considered, the method developed in this study exhibits significant time savings over the property lagging approach. In addition, maximizing the Newton solver's convergence rate by including sensitivities to the surface recession rate reduces the overall computational time when compared to excluding recession rate sensitivities.char ablation rate C h = corrected heat transfer Stanton number C h o = uncorrected heat transfer Stanton number C m = mass transfer Stanton number C p = specific heat at constant pressure, J=kg K C v = specific heat at constant volume, J=kg K _ E = element energy convection rate, W E = energy content, J e = specific internal energy, J=kg e = element h = specific enthalpy, J=kg k = thermal conductivity, W=m K L = time-dependent domain length, m _ m 00 = mass loss rate per unit area, kg=m 2 s N = shape function Pr = Prandtl number _ Q = element heat conduction rate, W Q = heat of ablation, J=kg _ q 00 = heat flux, W=m 2 _ q 00 = heat flux vector, W=m 2 R = residual r = recovery factor s = surface recession, m _ s = surface recession rate, m=s T = temperature, K t = time, s u = control volume boundary velocity, m=s u = velocity vector, m=s V = volume, m 3 x = coordinate with respect to instantaneous ablation front, m z = coordinate with respect to initial ablation front, m _ z = nodal velocity, m=s = thermal diffusivity, m 2 =s = temperature perturbation, K = emissivity = Landau coordinate = transformed temperature, K = blowing reduction parameter = local coordinate = density, kg=m 3 = Stefan-Boltzmann constant, W=m 2 K 4 = Stanton number correction Subscripts abl = ablation ah = aerodynamic heating back = back boundary blw = blowing cw = cold wall e = boundary layer edge condition full = full sensitivity matrix hw = hot wall iter = iterative solution procedure j = nodal index lag = property lagging solution procedure o = initial value r = recovery value rad = radiation ref = reference value res = reservoir property s = solid property tri = tridiagonal sensitivity matrix w = property of gases adjacent to the wall Superscripts n = time level = iteration level * = reference value