The thermal history of natural glasses is critical to understanding a wide range of geologic processes. Relaxation geospeedometry has been used to infer the cooling rates of naturally formed glasses across a wide range of compositions and geologic settings. However, using the Tool-Narayanaswamy (TN) geospeedometer is time consuming, requiring multiple isobaric heat capacity (C_P) measurements to constrain four sample-specific model parameters, before quantifying natural cooling history of a sample. Here we present a Monte Carlo-inspired numerical solver called CoolMonte, which automates the fitting procedure of experimental C_P measurements, and is capable of determining an unknown cooling rate using a single C_P measurement. We compare quantitative cooling rates of four naturally cooled obsidian lava samples determined using the traditional approach with multiple C_P measurements, to cooling rates determined using a single C_P measurement without sample-specific model calibration. Cooling rates calculated using a single C_P measurement are within 0.1 to 1.3 log₁₀ K s⁻¹ of cooling rates determined using multiple C_P measurements. We also assessed CoolMonte using 50 synthetic datasets with known cooling rates (≳0.1 K per year) and 10 previously published natural cooling rates which were reproduced within 0.8 log₁₀ K s⁻¹. CoolMonte reduces the time necessary to determine cooling rates of natural samples, improves the reproducibility of cooling rate estimates, and makes relaxational geospeedometry a more accessible method for the study of thermal histories of geologic systems.