In this report, we study the self-assembly of two silk-elastin-like proteins: one is a diblock S24E40 composed of 24 silk-like (S) repeats and 40 elastin-like (E) repeats; the other is a triblock S12C4E40, in which the S and E blocks are separated by a random coil block (C4). Upon lowering the pH, the acidic silk-like blocks fold and self-assemble into fibrils by a nucleation-and-growth process. While silk-like polymers without elastin-like blocks form fibrils by heterogeneous nucleation, leading to monodisperse populations, the elastin-like blocks allow for homogeneous nucleation, which gives rise to polydisperse length distributions, as well as a concentration-dependent fibril length. Moreover, the elastin-like blocks introduce temperature sensitivity: at high temperature, the fibrils become sticky and tend to bundle and aggregate in an irreversible manner. Concentrated solutions of S12C4E40 form weak gels at low pH that irreversibly lose elasticity in temperature cycling; this is also attributed to fibril aggregation.