We report on ultrasound and magnetization studies in three-dimensional, spin-dimerized Sr_{3}Cr_{2}O_{8} as a function of temperature and external magnetic field up to 61 T. It is well established [A. A. Aczel et al., Phys. Rev. Lett. 103, 207203 (2009)] that this system exhibits a magnonic-superfluid phase between 30 and 60 T and below 8 K. By mapping ultrasound and magnetization anomalies as a function of magnetic field and temperature we establish that this superfluid phase is embedded in a domelike phase regime of a high-temperature magnonic liquid extending up to 18 K. Compared to thermodynamic results, our study indicates that the magnonic liquid could be characterized by an Ising-like order but has lost the coherence of the transverse components.