L-ISW power spectrum from the covariance method simulation. The plot shows that the temperature power spectrum of the L-ISW simulations generated with the method described in Sect. 2.1 is compatible with the input theoretical power spectrum from CAMB and that the non-Gaussian contribution is always subdominant. The temperature power spectrum from one simulated L-ISW realization is shown in black, the red line refers to the theoretical input from CAMB while the blue refers to the non-Gaussian L-ISW contribution from the same realization.