Uniform bounds for the heat content of open sets in Euclidean space

We obtain (i) lower and upper bounds for the heat content of an open set in RmRm with R  -smooth boundary and finite Lebesgue measure, (ii) a necessary and sufficient geometric condition for finiteness of the heat content in RmRm, and corresponding lower and upper bounds, (iii) lower and upper bounds for the heat loss of an open set in RmRm with finite Lebesgue measure.