  Observational advancements are leading to increasingly precise measurements
of super-Earth masses and radii. Such measurements are used in internal
structure models to constrain interior compositions of super-Earths. It is now
critically important to quantify the effect of various model assumptions on the
predicted radii. In particular, models often neglect thermal effects, a choice
justified by noting that the thermal expansion of a solid Earth-like planet is
small. However, the thermal effects for water-rich interiors may be
significant. We have systematically explored the extent to which thermal
effects can influence the radii of water-rich super-Earths over a wide range of
masses, surface temperatures, surface pressures and water mass fractions. We
developed temperature-dependent internal structure models of water-rich
super-Earths that include a comprehensive temperature-dependent water equation
of state. We found that thermal effects induce significant changes in their
radii. For example, for super-Earths with 10 per cent water by mass, the radius
increases by up to 0.5$\,$R$_\oplus$ when the surface temperature is increased
from 300 to 1000$\,$K, assuming a surface pressure of 100$\,$bar and an
adiabatic temperature gradient in the water layer. The increase is even larger
at lower surface pressures and/or higher surface temperatures, while changing
the water fraction makes only a marginal difference. These effects are
comparable to current super-Earth radial measurement errors, which can be
better than 0.1$\,$R$_\oplus$. It is therefore important to ensure that the
thermal behaviour of water is taken into account when interpreting super-Earth
radii using internal structure models.
