This paper discusses whether the exergy destruction minimization or energy efficiency maximization comes first in resolving the climate emergency problem and provides sustainable solution options regarding the 2 nd Law of thermodynamics. It has been shown that low-temperature district energy systems with renewable energy sources and waste heat are effective in minimizing exergy destructions, while energy efficiency has a secondary impact. The research has been based on the Rational Exergy Management Model. The corresponding rational exergy management efficiency was directly related to nearly-avoidable CO2 emissions responsibility with a global magnitude of around 80% of direct emissions in the built environment. One conclusion deduced from such an unrecognized magnitude so far is that nearly-avoidable CO2 emissions may not be ignored anymore to develop new strategies for sustainable decarbonization, while the 1 st Law measures have limited remaining capabilities. New equations were developed to show the impact of exergy destructions on total CO2 emissions. Sample results show that a 30 percent-point decrease of exergy destructions comparing to the supplied exergy in thermo-mechanical systems has the potential of reducing total CO2 emissions by 35%. The paper argues that current exergy destruction is around 0.8 of the supply exergy, as an industry average, which gives ample room for improvement using the 2 nd Law, while the 1 st Law efficiency is already higher, and there is less room available for improvements concerning CO2 emissions. The paper shows that the 1 st Law efficiency may be increased by about 0.15 points, which gives a window of opportunity about a 25 percent-point decrease in emissions. The second main conclusion is that nowadays, new decarbonization strategies are needed based on the 2 nd Law, which will positively impact when coupled with the current 1 st Law measures towards meeting the Paris agreement.