Some rocks contain multiple remanence “components”, each of which preserves a record of a different magnetic field. The temperature ranges over which these remanence components demagnetize can overlap, making it difficult to determine their directions. We present a data analysis tool called Thermal Resolution Of Unblocking Temperatures (TROUT) that treats the process of thermal demagnetization as a function of temperature (or alternating field demagnetization as a function of coercivity). TROUT models the unblocking temperature distributions of components in a demagnetization experiment, allowing these distributions to overlap. TROUT can be used to find the temperatures over which paleomagnetic directions change and when two directional components overlap resulting in curved demagnetization trajectories. When applied to specimens given multi-component Thermoremanent Magnetizations (TRMs) in the laboratory, the TROUT method estimates the temperature at which the partial TRMs were acquired to within one temperature step, even for specimens with significant overlap. TROUT has numerous applications: knowing the temperature at which the direction changes is useful for experiments in which the thermal history of a specimen is of interest (e.g. emplacement temperature of pyroclastic deposits, re-heating of archaeological artifacts, reconstruction of cooling rates of igneous bodies). The ability to determine whether a single component or multiple components are demagnetizing at a given temperature is useful for choosing appropriate ranges of temperatures to use in paleointensity experiments. Finally, the width of the range of temperature overlap may be useful for inferring the domain state of magnetic mineral assemblages.