We present calorimetric experiments and specific‐heat Cp(T) measurements of 1‐butanol (n‐butanol) and of one of its chemical isomers, the secondary alcohol 2‐butanol (sec‐butanol), around its glass transition Tg as well as at low temperatures (1.6–30 K). We have obtained and measured both the glass and crystalline states of 1‐butanol, and the glass state of 2‐butanol which is an even better glass former. In this work, we focus on the comparative study of the calorimetric or thermodynamic properties of the glassy states of these two isomers of butanol, determining their glass‐transition temperatures, their discontinuities in specific heat at Tg, and the corresponding enthalpy fictive temperatures. At temperatures below 10 K, both isomers present the typical broad maximum for glasses in Cp/T3, often called the boson peak, its magnitude being much larger in 2‐butanol than in 1‐butanol.