Optical fibers are inherently designed to allow no interaction between the guided light and the surrounding optical radiation. Thus, very few optical fiber-based technologies exist in the field of optical radiation sensing. Accomplishing fully-distributed optical radiation sensing appears then as even more challenging since, on top of the lack of sensitivity explained above, we should add the need of addressing thousands of measurement points in a single, continuous optical cable. Nevertheless, it is clear that there exists a number of applications which could benefit from such a distributed sensing scheme, particularly if the sensitivity was sufficiently high to be able to measure correctly variations in optical radiation levels compatible with the earth surface. Distributed optical radiation sensing over large distances could be employed in applications such as Dynamic Line Rating (DLR), where it is known that solar radiation can be an important limiting factor in energy transmission through overhead power cables, and also in other applications such as thermo-solar energy. In this work, we present the proof-of-concept of the first distributed bolometer based on optical fiber technology and capable of detecting absolute changes of irradiance. The core idea of the system is the use of a special fiber coating with high emissivity (e.g., carbon coating or black paint). The high absorption of these coatings translates into a temperature change that can be read with sufficiently high sensitivity using phase-sensitive reflectometry. To demonstrate the concept, we interrogate distinct black-coated optical fibers using a chirped-pulse ΦOTDR, and we readily demonstrate the detection of light with resolutions in the order of 1% of the reference solar irradiance, offering a high-potential technology for integration in the aforementioned applications.