Crowded solutions of densely branched polymers with starlike architecture undergo a reversible gelation upon heating. This phenomenon is characterized by slow kinetics and is attributed to the formation of clusters causing a partial dynamic arrest of the swollen interpenetrating spheres at high temperatures. A kinetic pseudo-phase diagram of gelation temperature against the effective volume fraction is constructed. Stars with different functionalities exhibit a different sol-gel boundary; small differences in the internal structure of the stars (regular with spherical dense core vs irregular with nonspherical core but spherical overall shape) are presumably responsible for these differences. Thermal gelation is proposed as an alternative route to jamming of soft materials.