Analysis of the simple model proposed yields equilibrium curves in agreement with those obtained by other investigators for axially compressed, thin-walled, circular cylindrical shells. A rigorous calculation of the stability of the equilibrium of the model indicates that the snap-through phenomenon can be entirely absent when an imperfect shell is heated in a perfectly rigid testing machine. When the testing machine is sufficiently elastic, snap through will occur. It may take place at a temperature smaller than, equal-to, or greater than T = εcr/α, where εcr is the theoretical critical strain of the perfect shell and α is the coefficient of expansion of the material of the shell, but the maximum stress produced in the imperfect shell will always be less than εcrE, where E is Young’s modulus of the material.