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Thermonanophotonics, i.e. the study of photothermal effects in optical nanoantennas, has recently attracted growing interest. While thermoplasmonic structures enable a broad range of applications, from imaging and optofluidics devices to medical and photochemical systems, dielectric nanoantennas open new opportunities for thermo-optical modulation and reconfigurable metasurfaces. However, computing both photo-thermal and thermo-optical effects in large arrays of nanoantennas remains a challenge. In this work, we implement a fast numerical method to compute the temperature increase of multi-dimensional arrays of optical antennas embedded in a uniform medium, accounting for self-heating, collective heating as well as thermo-optical effects. In particular, we demonstrate scalable computation of temperature in 3D networks with $10^5$ particles in less than 1 hour. Interestingly, by explicitly considering the role of discrete nanoparticles on light attenuation and photothermal conversion, this approach enables the optimization of complex temperature profiles in 3D arrays. Importantly, we compute for the first time the impact of thermo-optical effects beyond the single nanoantenna. Our results show that collective heating contributions amplify these effects in multi-dimensional arrays of both Silicon and Gold nanospheres, highlighting the importance of considering them in photothermal calculations. Overall, the proposed method opens new opportunities for the rapid assessment of complex photothermal effects in arrays of optical nanoantennas, supporting the development of advanced thermonanophotonic functionalities.