Shear thickening of telechelic associating polymers, particularly of hydrophobically modified ethoxylated urethanes (HEURs), is classically attributed to either non-Gaussian behavior of the chains, also called finite extensible nonlinear elasticity (FENE), or to flow-enhanced formation of network strands; however, in a recent paper [Macromolecules, 45, 888 (2012)], Suzuki et al. show that neither of the previously mentioned interpretations can hold true, as they find shear thickening while at the same time the network structure has essentially remained the equilibrium one, except for the fact that reassociation to the network of the strands that continuously detach from it is anisotropically enhanced in the shear gradient direction. In the present paper, we propose a different mechanism that might explain shear thickening, namely, the stress contribution arising from the repulsive interaction between the flowerlike micelles that are forced to interpenetrate one another by the shear flow. In support of this idea is the fact that shear thickening is found only at low concentrations when the flowerlike micelles are nearly intact and essentially well-separated at equilibrium because relatively few bridging chains exist that percolate the network. Shear thickening is found to disappear with increasing concentration, possibly because micelles already interpenetrate at equilibrium, so that the flowerlike structure is reduced in favor of an increasing number of bridging chains. To develop the mathematical model in a simple way, the network of the bridging chains is here described by using a suitable dumbbell model. The dumbbell dynamics also regulates the repulsive micelle interactions. Predictions of the model qualitatively compare with the existing data, although for a better, more quantitative comparison, we suggest that Brownian simulations of the network of flowerlike micelles be developed.