We report the preparation of thermoresponsive macroporous polymer monoliths via high internal phase emulsions (HIPEs) where a polymerizable nonionic deep eutectic solvent served as the continuous phase. Mixtures of N-isopropylacrylamide (NIPAM) and acrylamide (AAm) in various mole ratios formed low melting point liquids that we term "polymerizable eutectics". In the presence of the nonionic surfactant Pluronic F127, stable oil-in-eutectic HIPEs are formed with hexadecane as the dispersed phase (80% v/v) and a continuous phase of the eutectic and a small amount of water. When the eutectic phase contained an initiator, RAFT chain transfer agent, and cross-linker, heating led to controlled polymerization and formation of a polyHIPE. The resulting monoliths had an interconnected porous network structure, significantly different to the equivalent structures produced from oil-in-water HIPEs, which exhibited a closed-cell morphology. The viscosity of the polymerizable eutectic and surfactant loading enabled the morphology, degree of openness, and mechanical properties of the polyHIPE to be readily tuned. When immersed in water, the monoliths exhibited temperature-dependent absorption of water due to the presence of NIPAM within the copolymer framework. Further, the inclusion of a RAFT chain transfer agent enabled subsequent surface polymerization from the polyHIPE to be realized, such that mechanical properties or surface wettability of the monolith could be varied while preserving the porous morphology. The tunable surface chemistry, porous structure, and mechanical properties of these monoliths present unique opportunities for applications as adsorbents, catalytic scaffolds, separation media, and so on.