Global annual average temperature is regarded as a precise indicator of the warming of the globe over centuries and if we track the available record on it, it is observed that the available period of 133 years (1980-2012) can be partitioned into three distinct phases, 1880-1936, 1937-1980 and 1981- 2012, based on temperature variation pattern (Pal et al., 2013). The content of the said paper deals with the development of models, parametric and nonparametric, which produce high precision levels (as measured by value of R2 coefficient) as high as 0.84. In this paper, a class of parametric models has been developed which is a combination of three mathematical functions, namely, cubic, exponential and trigonometric, respectively. An extensive search of models belonging to the abovementioned class identifies four different models whose R2 values lie within the range, 0.826 to 0.860 as a distinct improvement in the value of R2 vis-a-vis the precision level, over that obtained in Pal et al. (2013).