It is common knowledge that coupling to a heat bath, in general, tends to reduce the entanglement in a quantum system. In recent years, increasing interest has been devoted to the opposite situation where thermal or specifically tailored environments may stabilize or even generate entanglement. We prove the universality of this phenomenon for multipartite entanglement in the frame of an exactly solvable dephasing model. We show by evaluating analytical lower bounds for the appropriate entanglement measures that a common thermal environment can dynamically generate all entanglement classes of three qubits for almost any initial product state. For sufficiently weak dissipation this entanglement may persist up to arbitrarily large times.