A procedure to determine the critical temperature of a selected steel frame bearing structure is presented and discussed. This temperature, in case of fully developed fire, when the temperature of the exhaust gasses enveloping the structural members is equalized within the whole fire zone, may be considered as an impartial measure of safety. The obtained result does not depend on the heating progress but only on the static scheme and the load level in the considered structure. The quantitative and qualitative evaluation of the influence the joint stiffness decreasing in fire exerts on the resultant critical temperature constitutes the basic objective of the authors. It has been shown, that proceeding according to the recommended computational procedure does not necessarily result in an estimate fully unambiguous in interpretation. The critical temperature specified in a global mode, for the whole considered frame, is usually associated with a specific component of such frame, interpreted as the so called “weakest link”. Thus local loss of bearing capacity in such element is in this approach equivalent to the total destruction of the whole bearing structure. Indication, which of the components present in the considered frame should be treated as the critical one, because of its behaviour under fire conditions, seems to be a key to the forecast safety level warranted to the users of the structure. The authors show, that this association changes depending on the selected computational method, and this in turn substantially limits the reliability of the obtained estimate.