Studying the composition of exoplanets is one of the most promising approaches to observationally constrain planet formation and evolution processes. However, this endeavour is complicated for small exoplanets by the fact that a wide range of compositions are compatible with their observed bulk properties. To overcome this issue, we identify triangular regions in the mass–radius space where part of this intrinsic degeneracy is lifted for close-in planets, since low-mass H/He envelopes would not be stable due to high-energy stellar irradiation. Planets in these Hot Water World triangles need to contain at least some heavier volatiles and are therefore interesting targets for atmospheric follow-up observations. We perform a demographic study to show that only few well-characterised planets in these regions are currently known and introduce our CHEOPS GTO programme aimed at identifying more of these potential hot water worlds. Here, we present CHEOPS observations for the first two targets of our programme, TOI-238 b and TOI-1685 b. Combined with TESS photometry and published RVs, we use the precise radii and masses of both planets to study their location relative to the corresponding Hot Water World triangles, perform an interior structure analysis, and study the possible lifetimes of H/He and waterdominated atmospheres under these conditions. We find that TOI-238 blies, at the 1σ level, inside the corresponding triangle. While a pure H/He atmosphere would have evaporated after 0.4–1.3 Myr, it is likely that a water-dominated atmosphere would have survived until the current age of the system, which makes TOI-238 ba promising candidate for a hot water world. Conversely, TOI-1685 b lies below the mass–radius model for a pure silicate planet, meaning that even though a water-dominated atmosphere would be compatible both with our internal structure and evaporation analysis, we cannot rule out the planet being a bare core.