Solutions of multiblock nonionic polymers with hydrophobic blocks in water exhibit crystalline and liquid-crystalline phases over a narrow temperature range. This strong temperature sensitivity, critical in the design of novel self-assembled materials, is the result of the drastic increase of hydrophobicity combined with the weakening of solvating interactions (hydrogen bonding or dipolar) as the temperature is raised. In this paper, we separate thermal fluctuations into a "kinetic" temperature and solvation effects and parametrize temperature variations with a single parameter alpha, where the solvent is modeled implicitly. We provide a microscopic interpretation for this parameter, and molecular dynamics simulations are used to investigate the phases of short ABCBA pentablocks, where the A and C blocks are hydrophobic and the B blocks are hydrophilic but contain hydrophobic groups. At low temperatures and for increasing concentrations, the system undergoes a sol-gel transition. The gel is swollen and consists of highly interconnected spherical micelles with a finite lifetime. At higher temperatures, lamellar and perforated lamellar phases are found for increasing polymer concentrations, while for intermediate concentrations, the system is found in a supercoiled gel. We find good agreement of our results with modified and inverted Pluronic systems and discuss the relevance for other polymers including hydrophobic blocks such as telechelic or peptide-based polymers.