An analysis of the specific heat C of various amorphous solids at intermediate temperatures (1 K ≤ T ≤ 30 K) shows that the two parameters characterizing the maximum in C/T 3 vs. T , namely its height Pc and position Tmax, are related to each other as Pc ∝ T −1.6 max . Surprisingly, this relation is valid not only for all the amorphous solids whose intermediate-T specific heat can be found in the literature, but also for many of the corresponding crystalline solids. This suggests a general correlation between the mechanisms leading to the C/T 3 maximum in amorphous and crystalline solids. The established relation, together with the scaling property found earlier, contributes towards a unified understanding of the low-and intermediate-T properties of amorphous solids.