In this study we explore optical absorptance of single-layer hafnia dielectric coatings deposited on fused silica by ion beam sputtering technique. We investigate both linear and nonlinear absorptance by varying the laser intensity of 10 ps pulses at a 1 MHz repetition rate across wavelengths of 1064 nm, 532 nm, and 355 nm. Significant differences were observed between the as-deposited and thermally treated coatings. The as-deposited sample exhibited diminishing absorptance, while the thermally treated coatings showed an increase in absorption. Furthermore, our study delves into the strong impact of the pump wavelength on the nonlinear response. These findings bear potential significance in enhancing our understanding of the long-term effects in optical coatings. This understanding could prove crucial in the context of fatigue or laser-induced damage.