In nonhomogeneous differential equation $L(x)=f(x)$, related to the point thermal loaded Winkler beam, where L is a linear differential operator and load terms are appeared in $f(x)$, it is difficult to express the thermal load in $f(x)$. But with the aid of Generalized Functions, the thermal load can be described in $f(x)$ and the particular solutions are easily got. The magnitude of curvature at the thermal loading point is $frac{varepsilon}{h}$, where ${varepsilon}$ is the strain in top fiber and $h$ is the depth of beam. When the magnitude of curvature is "1", the solution is Green Function. This Green Function can be used and applied to get the other Green Functions in Free-end, Hinge and Fixed-end respectively. Finally we can get solutions of any types of thermal load using these Green Functions.