How to convert between different color maps on OpenCV?
I think it is a little more complicated than what is suggested in the comments, since you are dealing with temperatures. You need to revert the color mapping to a temperature value image, then apply one colormap with OpenCV that you like.
Going back to greyscale is not so straightforward as converting the image from BGR to greyscale, because you have colors like dark red that will may be mapped as dark grey as well as dark blue colors, however they are in totally opposite parts of the scale.
Both of your images are in different scale (temperature wise) as well, so, if you pass them back to grey scale, black is not the same temperature as the other one, so it is not possible to compare them directly.
To get a proper scale value you can try to get the upper rectangle (the one that shows the scale) and separate them in equal pieces and divide the temperature range with the same number of divisions. This will give you a color for each temperature. Then transform both images to cv::Mat double and each pixel will have the temperature value. 
Finally you must decide what will be your temperature range to decide the colors for all the images you have. For example you can choose 25-45. Then normalize the images with temperatures (the one with doubles) with the range you selected and normalize them to greyscale images (0 will be 25 and 255 will be 45) and apply the color map to this images. 
I hope this helps.
I have a set of thermal images which are encoded with different types of color maps.
I want to use a constant color map to make fault intelligence easier.
Please guide me on how to go about this.