A coupled Continuous and Hybridizable Discontinuous Galerkin method (CG-HDG) is used to perform the numerical simulation of a Glass Fiber Reinforced Polymer (GFRP) tubular cross-section exposed to fire. The problem statement is introduced by presenting the relevant governing equations and the GFRP material properties. As analytical solution is unavailable in this case, a method to estimate the discretization errors is presented. The considered problem is solved with different mesh sizes and time steps to compute the discretization errors and uncertainty in the numerical results for the quantities of interest. Thereafter, the problem is solved with high-order elements and it is shown that the results lie within the estimated uncertainty intervals. The problem is also solved with a coupled CG-CG method, where all the variables are discretized with CG, to compare the relative accuracy and efficiency of the coupled CG-CG and CG-HDG methods. Finally, the numerical results are compared with the experimental ones for the given quantities of interest.