The main purpose is to present the stochastic perturbation-based Finite Element Method analysis of the stability in the issues related to the influence of high temperature resulting from a fire directly connected with the reliability analysis of such structures. The thin-walled beam structures with constant cross-sectional thickness are uploaded with typical constant loads, variable loads and, additionally, a temperature increase and we look for the first critical value equivalent to the global stability loss. Such an analysis is carried out in the probabilistic context to determine as precisely as possible the safety margins according to the civil engineering Eurocode statements. To achieve this goal we employ the additional design-oriented Finite Element Method program and computer algebra system to get the analytical polynomial functions relating the critical pressure (or force) and several random design parameters; all the models are state-dependent as we consider an additional reduction of the strength parameters due to the temperature increase. The first four probabilistic moments of the critical forces are computed assuming that the input random parameters have all Gaussian probability functions truncated to the positive values only. Finally, the reliability index is calculated according to the First Order Reliability Method (FORM) by an application of the limit function as a difference in-between critical pressure and maximum compression stress determined in the given structures to verify their durability according to the demands of EU engineering designing codes related to the fire situation.