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We utilize a novel method to study the thermodynamics of two dimensional type0A black holes with constant RR flux. Our approach is based on theHamilton-Jacobi method of deriving boundary counterterms. We demonstrate thisapproach by recovering the standard results for a well understood example,Witten's black hole. Between this example and the 0A black hole we finduniversal expressions for the entropy and black hole mass, as well as theinfra-red divergence of the partition function. As a non-trivial check of ourresults we verify the first law of thermodynamics for these systems. Ourresults for the mass disagree with the predictions of a proposed matrix modeldual of the 0A black hole.Comment: 27 pages, uses utarticle.cls; corrected typos and added reference

Boundary counterterms and the thermodynamics of 2-D black holes