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In this paper we use linear combinations of n heat kernels to approximate solutions of the heat equation. In certain cases we are able to show that our approxi- For instance, for positive solutions of the heat equation such approximations are achieved using the theory of truncated moment problems. For general solutions of the heat equation, although approximations of this order is not guaranteed, a lower order approximation (e.g. of the order O(t ( 1 2p − n+1 2 ) ) ) is possible. Thesedoi:10.1137/08071778x fatcat:3cggi3g6jnar5iqebzgl7zrd3y