The thermal histories of terrestrial planets are investigated using two parameterized mantle convection models for either Earth like planets and planets with no active plate tectonics. Using parameterized models of mantle convection, we performed computer simulations of planetary cooling and volatile cycling. The models estimate the amount of volatile in mantle reservoir, and calculate the outgassing and regassing rates. A linear model of volatile concentration-dependent is assumed for the activation energy of the solid-state creep in the mantle. The kinematic viscosity of the mantle is thus dynamically affected by the activation energy through a variable concentration in volatile. Mantle temperature and heat flux is calculated using a model derived from classic thermal boundary layer theory of a single layered mantle with temperature dependent viscosity. The rate of volatile exchanged between mantle and surface is calculated by balancing the amount of volatiles degassed in the atmosphere by volcanic and spreading related processes and the amount of volatiles recycled back in the mantle by the subduction process. In the cases that lack plate tectonics, the degassing efficiency is dramatically reduced and the regassing process is absent. The degassing effect is dependent on average spreading rate of tectonic plates and on the amount of volatile in the melt extract in the transition zone between mantle and upper boundary laver. The regassing effect is dependent on the subduction rate and on the amount of volatile present on a hydrated layer on top of the subducting slab. The degassing and regassing parameters are all related to the intensity of the convection in the mantle and to the surface temperature of the planet, and they are regulated by the amount of volatiles in reservoir. Comparative study with the previous models display significant differences and improve the versatility of the model. The optimum efficiency factors found are in the range of 0.01-0.06 for degassing/regassing processes, in agreement with more recent estimates. An important effect of the volatile cycling process is a general negative feedback effect that results in a general trend to adjust the mantle volatile content in time to a value set by the energy balance in the system. As a result, the initial amount of volatile in the mantle is rendered irrelevant for late stage of thermal evolution. In the case of no plate tectonics, the opposite effect takes place: initial volatilization plays an important role through entire evolution. The implications of mantle convection on the stability of the lithosphere were investigated further using the thermal history calculations and numeric simulations. They point to the conclusion that mantle convection induced stress levels increase from the past to the present fact that leads to a greater potential of craton deformation. The main consequence of this trend is that sections of continental lithosphere that have remained stable since the Archean and Proterozoic are becoming progressively more prone to instability in the geologically modem era. After the volatiles are degassed from the mantle, they are cycled through the atmosphere. The interact with the climate influencing the surface temperature, and further controlling the mantle convection. Using a grey radiative-convective model for the atmosphere, we analyzed the feedback relationships between volatiles, especially water, and surface temperature. We showed that large amount of water degassed during a hot, possible melt ocean phase after the planet formation could conserve large amount of water in atmosphere and maintain the surface temperature at moderate level.