The prompt and delayed supercritical process of a nuclear reactor with temperature feedback is taken into consideration. The solutions of the point-reactor neutron kinetics equations under the condition of temperature feedback and negative inserted step reactivity are investigated. Different analytic models are given. The new solution is also proposed and compared with those published in literature. It is found that (1) the model and related solution for prompt supercritical can not be applied for the process of large negative inserted step reactivity; (2) under the condition of the same initial power the precursor prompt jump approximation model is better than the neutron prompt jump approximation model; and (3) the temperature prompt jump approximation model is always better than the precursor and neutron prompt jump approximation models for any initial power and negative inserted step reactivity, which is so far the most accurate analytical model.