Thermally activated processes are characterized by two key quantities, activation energy (Ea) and pre-exponential factor (ν0), which may be temperature dependent. The accurate measurement of Ea, ν0, and their temperature dependence is critical for understanding the thermal activation mechanisms of non-Arrhenius processes. However, the classic 1D Arrhenius plot-based methods cannot unambiguously measure Ea, ν0, and their temperature dependence due to the mathematical impossibility of resolving two unknown 1D arrays from one 1D experimental data array. Here, we propose a 2D Arrhenius plot method to solve this fundamental problem. Our approach measures Ea at any temperature from matching the first and second moments of the data calculated with respect to temperature and rate in the 2D temperature-rate plane, and therefore is able to unambiguously solve Ea, ν0, and their temperature dependence. The case study of deep level emission in a Cu(In,Ga)Se2 solar cell using the 2D Arrhenius plot method reveals clear temperature dependent behavior of Ea and ν0, which has not been observable by its 1D predecessors.