To understand the adsorption mechanism of methane in heterogeneous nanopore structures of coal, integral adsorption models based on linear, exponential, hyperbolic and quadratic energy distribution functions are established. The adsorption energy domain of the new models is assumed to be a finite interval. These new adsorption models can describe both the adsorption isotherm and the adsorption heat. A volumetric method of adsorption with a microcalorimetry system is used to measure the adsorption isotherms and integral heat, and then the parameters of the new models are obtained by fitting the experimental data. Since the adsorption heat can be different for different adsorption models, it is necessary to fit the adsorption isotherms and heat simultaneously. The fitting results of the adsorption isotherms and heat show that the new models are able to describe the experimental data better than the Langmuir model. By comparing the fitting results and the effective range of adsorption energy of the different adsorption models, it is shown that the exponential energy distribution function is the most reasonable model for methane adsorption in coals, which can be used to evaluate the energetic heterogeneity of nanopores in coal samples. The decreasing exponential energy distributions of three coal samples indicate that a larger adsorption energy corresponds to fewer adsorption sites in the coal samples. The proportion of high adsorption energy is related to the micro-nanopore volume in the coal samples.