Initially, you have to interpolate the available temperature distribution to the entire output image.
You can use any of the interpolation methods to create the interpolated values.
Based on the new temperature(interpolated) values, you have to apply a color map.
You have to prepare a map(RGB lookuptable for each temperature ) starting from black(0)->blue(49)->green(69)->yellow(68)->red(107) at last.
This map should have a smooth transition from one color to other. ie, Index 59 of the map should indicate a transitaion from blue to green.
The following library will be helpful to create such gradients.
I'm not sure which is the good method for interpoaltion, Bi-Cubic interpolation or any other interpolation can be used to create the temperature distribution of the entire image from less number of inputs.