The thermal history modeling software HeFTy is one of several widely used tools for the numerical analysis of low-temperature thermochronologic data. HeFTy version 2 includes a new optional Controlled Random Search (CRS) strategy for posing the candidate time-temperature (tT) paths that are tested against data. Unlike the Monte Carlo (MC) strategy that is the default algorithm, the CRS procedure attempts to converge toward a solution. In order to overcome known limitations of CRS convergence (e.g., returning an artificially narrow range of tT solutions that exaggerates the capacity of the data to document a specific thermal history), this ‘enhanced’ CRS randomizes, expands, and reconverges on candidate tT-paths. Here, we use both synthetic and real apatite and zircon (U-Th)/He data, previously analysed using the MC algorithm in HeFTy, to explore the utility of this new tool. Overall, we demonstrate that the enhanced CRS can substantially improve computation time and is useful for finding families of tT paths that fit thermochronologic data. However, users should still expect the CRS to produce an uneven distribution of paths (i.e., ‘clustering’) in the permissible tT space. Therefore, we suggest that systematically performing multiple CRS and/or MC inversions is essential for building a robust assessment of how CRS inversion results are produced by the data and inversion design choices, or else it may not be clear what features of a CRS result are produced by the convergence algorithm rather than the data and a sample’s geologic context. Diagnosing such behaviors is essential for using thermal history inversion results for geological interpretations.