Synthesis of the first RNAs represents one of the cornerstones of the emergence of life. Recent studies demonstrated powerful scenarios of prebiotic synthesis of cyclic nucleotides in aqueous and formamide environments. This raised a question about their thermodynamic stability, a decisive factor determining their accumulation in a prebiotic pool. Here we performed ab initio molecular dynamics simulations at various temperatures in formamide and water to study the relative stabilities of the 2',3' and 3',5' isomers of cyclic nucleotides. The computations show that in an aqueous environment 2',3' cyclic nucleotides are more stable than their 3',5' counterparts at all temperatures up to the boiling point. In contrast, in formamide higher temperatures favor the accumulation of the 3',5' cyclic form, whereas below about 400 K the 2',3' cyclic form becomes more stable. The latter observation is consistent with a formamide-based origin scenario, suggesting that 3',5' cyclic nucleotides accumulated at higher temperatures subsequently allowed oligomerization reactions after fast cooling to lower temperatures. A statistical analysis of the geometrical parameters of the solutes indicates that thermodynamics of cyclic nucleotides in aqueous and formamide environments are dictated by the floppiness of the molecules rather than by the ring strain of the cyclic phosphodiester linkages.