The Global Warming Potential-star (GWP*) approach is a way to account for the contributions of non-CO2 emissions in the carbon budget framework. It is an active research question to what extent the carbon budget approach holds under overshoot scenarios. Here we evaluate the performance of GWP* in the carbon budget framework under long-term overshoot scenarios by converting CH4 emissions to CO2-equivalent emissions via GWP* and calculating the temperature through simple climate models. We show that the use of GWP* can lead to an overestimation or underestimation of temperatures over multiple centuries, depending on the rate of CH4 emission decline. Furthermore, our model simulations indicated that the use of GWP* further contributes to an overestimation of the transient climate response to cumulative CO2 emissions (TCRE) under decreasing CO2-equivalent emissions, converted from CH4. The applicability of GWP* needs to be assessed in overshoot scenarios further by exploring the uncertainties in the representation of Earth System feedbacks.