The record on the data on global annual average temperature over the last thirty two years presents a continuous increase (though very mild) in temperature over years and this warming of the globe is, indeed, a matter of deepest concern to all of us at the moment. It is required to develop appropriate measures to contain the temperature-rise and when such measures (which perceptibly and most satisfactorily address the problem) are created, it is our mandate to implement those holistically in order to save the human civilization from a perilous future. Global temperature models expose the inherent trend existing in the temperature-record. A literature-survey on modelling of global temperature reveals the following articles, Pal and Pal, 2011, Pal et al. (2013) and Pal et al. (2014), wherein the precision levels (in terms of R2 values) of the models did not exceed 0.89.This paper presents superior global annual average temperature models (parametric based on mathematical functions) with precision levels (in terms of R2 values) varying in the range, 0.875 to 0.940.