Water-in-oil-in-water (W/O/W) emulsions can be designed to encapsulate, protect, and release both hydrophilic and hydrophobic functional compounds. In this study, we examined the impact of crystallizing the fat phase on the resistance of W/O/W emulsions to osmotic stress, with the aim of developing osmotic-responsive systems. Polyglycerol polyricinoleate (PGPR) was used as a hydrophobic surfactant to stabilize the inner water droplets, while Quillaja saponin and whey protein isolate (WPI) were used as hydrophilic surfactants to coat the oil droplets. The impact of fat crystallization was examined by using either a liquid (soybean oil, SO) or semi-solid (hydrogenated soybean oil, HSO) fat as the oil phase. An osmotic stress was generated by establishing a sucrose concentration gradient between the internal and external water phases. Alterations in the droplet size, morphology, and stability of the W/O/W emulsions was measured when the sucrose concentration gradient was changed. The W/O droplets in the SO-emulsions swelled/shrank when the external sucrose concentration was below/above the internal sucrose concentration, which is indicative of water diffusing into/out of the droplets. Conversely, there was no change in the size of the W/O droplets in the HSO-emulsions under the same conditions, which was attributed to the mechanical strength of the fat crystal network resisting swelling or shrinking. HSO-emulsions did exhibit swelling when they were heated above a critical temperature, due to melting of the fat crystals and disruption of the crystal network. Our results demonstrate that crystallization of the oil phase of W/O/W emulsions can prevent water transport due to osmotic stress, which may be useful for developing temperature-triggered delivery systems for application in foods, cosmetics, pharmaceuticals, or personal care products.