Recent advancements in single-photon detection, such as Single-Photon Avalanche Diodes (SPADs), have enabled picosecond-resolution measurements of photon arrival times. These technologies are crucial for applications like Satellite Laser Ranging (SLR) and Intensity Interferometry (II), where atmospheric effects on photon propagation remain a key uncertainty during observations of remote sources outside of the Earth's atmosphere. Previous studies predicted 30-ps temporal fluctuations in photon arrival times due to atmospheric turbulence, potentially impacting high-precision timing experiments. In this work, we investigate effects of the atmospheric broadening on zero-baseline intensity interferometry measurements on a telescope with the Sun, as a thermal non-coherent light source. We establish an upper limit of 6-ps RMS on the broadening of the Hanbury Brown and Twiss (HBT) peak induced by the atmosphere during such observations. We discuss techniques to measure non-zero baseline effects of atmosphere widening and provide estimations from theoretical considerations.