Heat capacities (C) of 3He submonolayer solids adsorbed on a graphite surface are measured down to 100 μK, a factor of twenty lower temperatures than previous work. At a real densities near the commensurate √3 × √3 solid (6.4 nm−2), an anomalous temperature dependence, C ∝ 1/T, is observed in a wide temperature range over two orders of magnitude (0.1 ≤ T ≤ 20mK). Similar behavior was observed for the commensurate √7 × √7 solid in the second-layer with the same density, suggesting a common microscopic mechanism. It is, however, a puzzle that the √3 × √3 solid is ferromagnetic according to recent magnetization measurements by ISSP group, while the √7 × √7 solid is known to be antiferromagnetic. Possible explanations for this conflict, such as vacancy effects or multiple-spin exchanges modulated by a substrate potential corrugation, are discussed.