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<jats:title>ABSTRACT</jats:title> <jats:p>Recent measurements of hot and cold spots on the cosmic microwave background (CMB) sky suggest the presence of super-structures on (&gt;100 <jats:italic>h</jats:italic> <jats:sup>−1</jats:sup> Mpc) scales. We develop a new formalism to estimate the expected amplitude of temperature fluctuations due to the integrated Sachs–Wolfe (ISW) effect from prominent quasi-linear structures. Applying the developed tools to the observed ISW signals from voids and clusters in catalogs of galaxies at redshifts <jats:italic>z</jats:italic> &lt; 1, we find that they indeed imply a presence of quasi-linear super-structures with a comoving radius of 100 ∼ 300 <jats:italic>h</jats:italic> <jats:sup>−1</jats:sup> Mpc and a density contrast |δ| ∼ <jats:italic>O</jats:italic>(0.1). We also find that the observed ISW signals are at odds with the concordant Λ cold dark matter model that predicts Gaussian primordial perturbations at ≳3σ level. We confirm that the mean temperature around the CMB cold spot in the southern Galactic hemisphere filtered by a compensating top-hat filter deviates from the mean value at ∼3σ level, implying that a quasi-linear supervoid or an underdensity region surrounded by a massive wall may reside at low redshifts <jats:italic>z</jats:italic> &lt; 0.3 and the actual angular size (16°–17°) may be larger than the apparent size (4°–10°) discussed in literature. Possible solutions are briefly discussed.</jats:p>