We present first direct evidence of modulation in the $K$-band of Blazhko-type RR Lyrae stars that are identified by their secular modulations in the I-band data of OGLE-IV. A method has been developed to decompose the $K$-band light variation into two parts originating from the temperature and the radius changes using synthetic data of atmosphere-model grids. The amplitudes of the temperature and the radius variations derived from the method for non-Blazhko RRab stars are in very good agreement with the results of the Baade-Wesselink analysis of RRab stars in the M3 globular cluster confirming the applicability and correctness of the method. It has been found that the Blazhko modulation is primarily driven by the change in the temperature variation. The radius variation plays a marginal part, moreover it has an opposite sign as if the Blazhko effect was caused by the radii variations. This result reinforces the previous finding based on the Baade-Wesselink analysis of M3 (NGC 5272) RR Lyrae, that significant modulation of the radius variations can only be detected in radial-velocity measurements, which relies on spectral lines that form in the uppermost atmospheric layers. Our result gives the first insight into the energetics and dynamics of the Blazhko phenomenon, hence it puts strong constraints on its possible physical explanations.
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