Parabolic Partial differential equations are widely used in Physical Science. A familiar example is the Heat Conduction Equation or Diffusion Equation. But such equations with time variant coefficients are very useful in Physics as well as in Molecular Biology. With that hope in mind we tried to vary the various coefficients with time and solved to get the Temperature data. We then applied Regression, One and two Way ANOVA to make a Statistical analysis of that. We had also used MONTE-CARLO Simulation Model for some cases.