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The present paper reports a thorough statistical elucidation of the time series of surface temperature in monthly as well as seasonal scale over eastern India during pre-monsoon (March-May) and summer monsoon (June-September) in India. Climate risk is a challenge to millions of people whose livelihood is dependent on agriculture. Considering data for the period of 1901-2007, the autocorrelation functions for both the seasons have been investigated for persistence and an absence of long-term memory has been detected in all the cases. The intrinsic uncertainty has been quantified through Shannon-entropy by framing an appropriate probability distribution and the entropy has been computed for monthly as well as seasonal scales. Finally, using rescaled range analysis, the Hurst exponents have been computed and finally the surface temperature time series has been observed to be anti-persistent for pre-monsoon and Brownian for summer-monsoon months.