Cryogenic transmission electron microscopy (Cryo-TEM) provides direct visualization of bicontinuous sponge (L₃) phases, where a surfactant bilayer meanders through space, dividing solvent into two continuous domains. Temperature increase destabilizes lamellar order by lowering the bending rigidity and driving the Gaussian modulus toward values that favor handle formation. We captured this transition as the loss of layered registry and the emergence of a labyrinthine bilayer network rich in saddle regions. A Cahn-Hilliard-type phase-field model reproduces these features: small shifts in the free-energy landscape and interfacial penalty are sufficient to convert stripe-like lamellae into bicontinuous structures. This synergy between imaging and modeling highlights how thermal fluctuations push membranes into topologies inaccessible at lower temperatures, offering a predictive framework for designing temperature-responsive surfactant systems.