Temperature dependences of molecular line-shape parameters are important for the spectroscopic studies of the atmospheres of the Earth and other planets. A number of analytical functions have been proposed as candidates that may approximate the actual temperature dependences of the line-shape parameters. In this article, we use our ab initio collisional line-shape calculations for several molecular systems to compare the four temperature ranges (4TR) representation, adopted in the HITRAN database [J. Quant. Spectrosc. Radiat. Transfer 2017;203:3] in 2016, with the double-power-law (DPL) representation. Besides the collisional broadening and shift parameters, we consider also the most important line-shape parameters beyond Voigt, i.e., the speed dependence of broadening and shift parameters, and real and imaginary parts of the complex Dicke parameter. We demonstrate that DPL gives better overall approximation of the temperature dependencies than 4TR. It should be emphasized that DPL requires fewer parameters and its structure is much simpler and more self-consistent than the structure of 4TR. We recommend the usage of DPL representation in HITRAN, and present DPL parametrization for Voigt and beyond-Voigt line profiles that will be adopted in the HITRAN database. We also discuss the problem of the Hartmann-Tran profile parametrization in which the correlation parameter, η, and frequency of the velocity-changing collisions parameter, νvc, diverges to infinity when collisional shift crosses zero; we recommend a simple solution for this problem.