Adsorption Heat Transformation (AHT) is one of the most promising solutions for reducing the consumption of fossil fuels and effective environmental protection. The working pair “adsorbent – adsorbate” is a key factor affecting the performance of AHT cycle. This paper addresses the investigation of the adsorption of methanol vapor on MIL-101(Cr), which belongs to a family of porous crystalline solids, Metal – Organic Frameworks. MIL-101(Cr) is shaped with polyvinyl alcohol (PVA) as a binder to form grains. The equilibrium of methanol adsorption on the grains of MIL-101(Cr) is studied and the potential of the MIL-101(Cr) – methanol working pair is estimated for various AHT cycles. The dynamics of methanol adsorption is explored under conditions of a new cycle for upgrading temperature of ambient heat. The main findings of this study are: (i) the addition of PVA does not affect methanol adsorption equilibrium; (ii) the amount of methanol exchanged under typical conditions of the cooling and ambient heat amplification cycles varies from 0.27 to 0.31 g/g; (iii) under conditions of the heat amplification cycle the methanol adsorption on the loose grains of 0.8–1.8 mm size, occurs under the “grain size insensitive mode” when the dynamics of adsorption in the adsorbent beds with the same thickness does not depend on the size of MIL grains. For the desorption runs, the poor mass transfer decelerates the process for the grains of 1.6–1.8 mm size; (iv) the specific useful heat and heating power for heat amplification cycle equal 385 kJ/kg and 0.65–1.95 kW/kg, respectively. The high values of specific heat and heating power illustrate an encouraging potential of the “MIL-101(Cr) – methanol” pair for the ambient heat amplification cycle.