We have examined the stability of the ''quasi-static'' models of coronal loops. We find that all models in which the heat flux at the base of the loop is assumed to vanish are unstable to the growth of thermal perturbations. The growth rates and the profiles of the unstable modes indicate that the instability involves primarily the low-temperature, transition-region plasma. The models can be made stable only by assuming that the heat flux at the base of the loop is large, of the order of 13% of the maximum flux in the loop. Our results imply that the transition region must be intrinsically dynamic.