The Global Warming Potential (GWP) and recent Global Temperature Potential (GTP) concepts are widely used not only for research but also for economical and even political evaluations of greenhouse gas and other climate forming factor effects in the current climatic change. The proposal to replace or add the GWP and Radiative Forcing (RF) by the GTP with usage of actual temperature of the ground surface air requires the additional information on the thermal sensitivity of the various parts of climatic system for different time periods of external actions. The proposed improvements of these climate parameters may and will be used in the current and future assessment in IPCC and other international reports. The examples of RF, GWP, and GTP evaluation for methane, NOx and especially for halocarbons under the Montreal Protocol restrictions will be presented and discussed. The future development of the above presented indices in particular for the IPCC and the Kyoto Protocol purposes is proposed, together with some corrections to the GTP evaluation to account the energy exchange between the lower troposphere and the ocean layers having various heat capacity values