Could a heavy exoplanet squeeze water into being liquid and 4° warm?
Hardly. Maybe. Probably. It depends.
Liquid water at atmospheric pressure is densest at 4°C - but that is a function of pressure and temperature.
The phase of a material (solid, liquid, gas, critical) depends on both, pressure and temperature - and so does the density which depends on both, linearily within one phase, discontinuous at phase boundaries. The phase diagramme of water which describes the phase you find for any combination of temperature and pressure is surprisingly complex for water and thus one of the least well-established ones.
Maybe one can answer your question already with a clear 'yes', if you consider a sub-surface ocean an acceptable answer. Enceladus' interior is somewhat heated by tidal interaction with Saturn. From Cassini observations we know that under about a 30km thick ice sheet on Saturn's moon Enceladus we have an ocean of liquid saline water - a source for the geysir activity on that moon.