Collisional cooling of primordial and interstellar media by H2

8 pags., 10 figs., 2 tabs.We have computed the rate of collisional cooling of a gas by H2 molecules under conditions appropriate to the primordial and interstellar media. We incorporated the results of recent calculations of the rate coefficients for collisional excitation of H2 by H and H+, which are essential to a reliable evaluation of the ortho:para H2 ratio and the cooling rate. Comparison is made with the results of previous calculations of the cooling function. The data are made available for grids of values of the kinetic temperature, density, H:H2 ratio, and the fractional abundance of H+, together with a programme to perform linear interpolation of the data sets for any given set of values of these parameters, within the ranges of the grids.This project received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 811363). We acknowledge the Programme National Physique et Chimie du Milieu Interstellaire (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES. FL acknowledges financial support from the Institut Universitaire de France. TG-L acknowledges support from project no. FIS2017-83157-P (MINECO/AEI/FEDER, UE). DRF acknowledges support from STFC (ST/L00075X/1), including provision of local computing resources