No, emitting thermal energy at the same rate does not necessarily mean that both objects have the same temperature. The rate at which an object emits thermal energy depends on its temperature and other factors such as its surface area, emissivity, and surroundings.
Temperature is a measure of the average kinetic energy of the particles within an object. Objects with different temperatures have different average kinetic energies. When two objects are in thermal contact, heat transfer occurs between them. Heat transfer happens from the object with a higher temperature to the object with a lower temperature until they reach thermal equilibrium.
If two objects are emitting thermal energy at the same rate, it suggests that they are likely in thermal equilibrium with each other. In other words, the rate at which they gain and lose heat is balanced, and their temperatures are not changing over time. However, this does not mean that both objects have the same temperature. It is possible for them to have different temperatures as long as the rate of heat transfer between them is equal.
To determine whether two objects have the same temperature, you would need to measure their temperatures directly using a thermometer or another suitable temperature measurement device.