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I'm afraid your wrong here, and I don't need fancy math to prove it. If you add energy to a system in pulses, as the Earth gets energy from the sun, at first the system's average temperature will rise but only until equilibrium is reached. Equilibrium is reached when the amount of heat lost between pulses (at night say)is equal to the amount added during a pulse (during the day). Earth, on average, is in equilibrium. Some days more heat is added than lost, sometimes less. This is why some days are warmer than others. If heat is retained in the Earth system then the Earth will become warmer every day.It does seem that right now Earth is getting warmer. This however is simply short term. On average, on time scales of millions of years, the temperature stays very much the same.
"If you add energy to a system in pulses, as the Earth gets energy from the sun, "The earth does not receive energy from the sun in pulses.The sun doesn't switch on and off.