The temperature of the interstellar medium (ISM) is governed by several physical process, among which radiative line cooling, external UV/cosmic ray heating, and the mechanical work of compression and expansion. In regimes where the dynamical effect is important, the temperature deviates from that derived by simply balancing the heating and cooling functions. We hereby present a collapse solution that describes a clump that is contracting and losing energy through radiation. This yields an effective equation of state (eos) that can be generally applied to various ISM context, where the cooling function is available from first principles, and expressed as powerlaw product of the density and temperature. Our findings suggest that a radiatively cooing gas under self-gravitating collapse and easily manifest an effective isothermal eos. This model provides theoretical justification for the simplifying isothermal assumptions of simulations at various scales, and can also provide a more relistic thermal recipe without additional computation cost.