The composite operator TT̅, obtained from the components of the energy-momentum tensor, enjoys a quite general characterization in two-dimensional quantum field theory also away from criticality. We use the form factor bootstrap supplemented by asymptotic conditions to determine its matrix elements in the sinh-Gordon model. The results extend to the breather sector of the sine-Gordon model and to the minimal models M_2/(2N+3) perturbed by the operator φ_1,3.