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We present a method to build magnetic models for insulators based onhigh-temperature expansions by fitting both the magnetic susceptibility and thelow temperature specific heat data. It is applied to the frustrated magnetkapellasite (Cu3Zn(OH)6Cl2) with the J1-J2-Jd-Heisenberg model on the kagomelattice. Experimental data are reproduced with a set of "competing" exchangeenergies closed to J1 = -12K, J2= -4K and Jd=15.6K, where Jd is the thirdneighbor exchange energy across the hexagon. Strong constrains between theseexchange energies are established. These values confirm the results of B.F{\aa}k et al. (Phys. Rev. Lett., 109, 037208 (2012)) regarding the location ofkapellasite in the {\it cuboc2} phase of the Heisenberg model. The quality andlimits of this modeling are discussed.

Exchange energies of Kapellasite from high-temperature series analysis of the kagome lattice J1-J2-Jd-Heisenberg model