An analytical method for calculation of minimum quench energies (MQEs) of uncooled composite low temperature superconductors is presented. The method takes into account transient heat transfer in the conductor as well as temperature dependent ohmic heat generation and temperature dependent thermophysical properties of the conductor. MQE of the conductor is calculated based on the analysis of evolution of peak temperature in the normal zone. The method is validated by comparison of the obtained results with the experimental data as well as with analytical and numerical results taken from literature.