Computer servers can be represented by lumped thermal capacitances for the purpose of simulating server and data center transient thermal response to changes in operating conditions or equipment failures. Two parameters are needed to characterize the transient behavior of a lumped-capacitance server: its thermal capacitance and its thermal conductance, heat transfer effectiveness, or time constant. To avoid the laborious task of obtaining these parameters from measurements or estimations of the thermal characteristics of internal components of the server, a method is proposed to derive these parameters from external measurements that can be easily obtained without performing an "autopsy" on the server. In this paper, we present the mathematical formulation underlying the proposed method and describe how the parameters are to be obtained from external air-temperature measurements using the mathematical model. We then present validation test cases using experimental data from server shut-down and inlet-temperature ramp tests. The experimentally obtained parameters are implemented into a computational fluid dynamics (CFD) case study of server shutdown in which the transient server exit air temperature is computed from the lumped-capacitance parameters via a user-defined function. The results thus obtained are in excellent agreement with the experimental data.