An adaptive parallel tempering algorithm is developed in a user-friendly fashion that efficiently and robustly generates near-optimum solutions. Using adaptive, implicit, time-integration methods, the method allows fitting model parameters to dynamic data. The proposed approach is relatively insensitive to the initial guess and requires minimal fine-tuning: most of the algorithm parameters can be determined adaptively based on the analysis of few model simulations, while default values are proposed for the few remaining ones, the exact values of which do not sensitively affect the solution. The method is extensively validated through its application to a number of algebraic and dynamic global optimization problems from Chemical Engineering literature. We then apply it to a multi-parameter, highly nonlinear, model of the rheology of a thixotropic system where we show how the present approach can be used to robustly determine model parameters by fitting to dynamic, large amplitude, oscillatory stress vs. shear rate, data. (c) 2016 American Institute of Chemical Engineers AIChE J, 63: 1937-1958, 2017