We study transient networks formed by monodisperse telechelic polypeptides with collagen-like end blocks and a random-coil-like middle block. These artificial proteins are created using recombinant DNA techniques. Upon cooling, the end blocks associate reversibly into triple helices, leading to gels with a well-defined junction multiplicity of three. Both the storage modulus and the relaxation time of the gel increase very strongly as a function of concentration, and decrease with increasing temperature. All the experimental results are described quantitatively by an analytical model, based on classical gel theory, that requires no adjustable parameters, and accounts for the molecular structure of the gel, and the presence of loops and dangling ends.