A quantum point contact was used to observe single-electron fluctuations of a quantum dot in a GaAs heterostructure. The resulting random telegraph signals (RTS) contain statistical information about the electron spin state if the tunneling dynamics are spin dependent. We develop a statistical method to extract information about spin-dependent dynamics from RTS and use it to demonstrate that these dynamics can be studied in the thermal energy regime. The tunneling rates of each spin state are independently measured in a finite external magnetic field. We confirm previous findings of a decrease in overall tunneling rates for the spin excited state compared to the ground state as an external magnetic field is increased.