Thermal instability (TI) is a trigger mechanism, which can explain formation of condensations through some regions of the interstellar clouds. Our goal here is to investigate some conditions for occurrence of TI and formation of pre-condensations through the outer half a quasi-static spherical molecular clump or core. The inner half is nearly singular and ambiguous so out of scope of this research. We consider a spherically symmetric molecular cloud in quasi-static and thermally equilibrium state, and we use the linear perturbation method to investigate occurrence of TI through its outer half. The origin of perturbations are assumed to be as Inside-Rush-Perturbation (IRP) with outward perturbed velocity at inner region of the cloud, and Outside-Rush-Perturbation (ORP) with inward perturbed velocity originated at the outer parts of the cloud. The local thermal balance at the outer half of the molecular cloud leads to a local loosely constrained power-law relation between the pressure and density as $p \propto \rho^{1+\chi}$, where $-0.4\lesssim \chi\lesssim 0.05$ depends on the functional form of the net cooling function. Physically, the value of $\chi$ depends on the power of dependence of magnetic field to the density, $\eta$, and also on the value of magnetic field gradient, $\zeta$. For strong magnetic field (smaller $\eta$) and/or large field gradient (greater $\zeta$), the value of $\chi$ decreases, and vice versa. The results show that increasing of the value of $\chi$ leads to form a flatter density profiles at the thermally equilibrium outer half of the molecular clump or core, and to occur more thermally unstable IRP and ORP with smaller growth time-scales, and vice versa.
