An apparatus includes a coldplate configured to be thermally coupled to a structure to be cooled and to remove thermal energy from the structure. The coldplate includes (i) first and second outer layers having at least one first material and (ii) a third layer embedded in the outer layers and having at least one second material. The first and second materials have different coefficients of thermal expansion (CTEs). The third layer is embedded non-uniformly in the outer layers so that different zones of the coldplate have different local CTEs. The third layer may include openings extending through the second material(s), and projections of the first material(s) from at least one of the first and second outer layers may partially or completely fill the openings. The first and second outer layers may include aluminum or an aluminum alloy, and the third layer may include aluminum silicon carbide or thermal pyrolytic graphite.