Once again, nonsense. As energy is retained within the system, this causes the temperature to rise. The energy radiated by a black body is, according to the Stefan-Boltzmann law, j=\sigma T^4, where T is the temperature in Kelvin and \sigma is the Stefan–Boltzmann constant. Since the energy radiated increases as the fourth power of the temperature, a modest increase in temperature can balance a substantial increase in energy. Energy cannot “run away” or “accumulate” in an open system because it will simply lead to an increase in temperature causing the energy to be radiated away. Thus, increasing the energy in the system raises its equilibrium temperature and amount of energy it radiates.
There are no sealed bins in the system that are locked away from one another. All of the energy sources and sinks connect to one another and will eventually reach thermal equilibrium after a perturbation. The global energy budget can be modeled very simply as a system where essentially all of the energy input comes from the Sun and all energy output is eventually radiated to space in the infrared. The mean temperature of the planet will be the value which causes energy radiated to equal energy absorbed. The internals of the system may be very complicated and have all kinds of feedback loops, nonlinear interactions, reservoirs, and delays, but regardless of these details “the books gotta balance” and that’s what determines temperature.
Non-solar energy inputs (geothermal, tidal, nuclear fission, etc.) are, as described in this comment from 2021-11-22, negligible on the scale of the global energy budget.