Calorimetric measurements of the glass transition temperatures (T_g) of hydrous carbonate melts are reported on a near-eutectic composition of 55 mol% K₂CO₃– 45 mol% MgCO₃with up to 42 mol% bulk H₂O dissolved in the carbonate melt. Hydrous melts were quenched from 750°C to transparent and crystal-free glasses and were subsequently analysed for water content before and after measuringT_gby high-sensitivity differential scanning calorimetry. The glass transition and limited fictive temperatures as a function of the water content were determined at 10 K/min cooling/heating rates resulting inT_granging from 245°C at nominally anhydrous conditions to 83°C in the presence of 42 mol% H₂O in the glass. Through a generalized Gordon–Taylor analysis, the factorsk(7.27),k₀(3.2) and the interaction parameterA_x(0.49) were derived. The limited fictive temperature of a hypothetically, zero water containing 55 mol% K₂CO₃– 45 mol% MgCO₃glass is 232 ± 5°C (505 K). The high value of the interaction parameterAindicates strong specific molecular interactions between water and the carbonates in the glassy state and a large decrease in the excess enthalpy of mixing during the conversion of the glassy into the liquid state at the glass transition.This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 1)'.