We report on the direct thermal conductivity measurement of nanoscale nanolaminate material system from metallic thin-film (Al) and carbon-based low-dimensional material (swCNT). Such accurate measurement was made possible by realizing submicron measurement platform using micromaching techniques. Furthermore, by measuring the resonant response of such nanomechanical structures, we are able to deduce their thermal-elastic properties. We find that addition of swCNTs to Al thin-film greatly suppresses the overall coefficient of thermal expansion. On the other hand, addition of swCNTs has marginal effects on the resulting thermal conductivities.