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A positive measurable function K on a domain D in ${ℝ}^{n+1}$ is called a mean value density for temperatures if $u(0,0)=\int {\int }_{D}K(x,t)u(x,t)dxdt$ for all temperatures u on D̅. We construct such a density for some domains. The existence of a bounded density and a density which is bounded away from zero on D is also discussed.