We employ the variational principle of calculus and continuum approximation approach to generate a useful dynamical equations to describe the dynamics of deoxy-ribonucleic acid (DNA). Based on the choice of temperature dependent potential function, we establish a better understanding of the effect of variations in temperature $T$ on the dynamics of the underlying system. The mathematical model yields a wave packet solution whose nonlinear superposition gives a special kind of "radiative breather soliton" possessing the periodic lossless energy transfer property. The findings show the existence of breathers in DNA dynamics and provide clear reaffirmation of solitary waves in the behaviour of DNA.