MATLAB: Saving grayscale image as it appears in jet colormap of imagesc


Hello, I have a grayscale TIF images (although it says it is TrueColor, nevermind). I need to convert them to grayscale and save it as it appears in imagesc(), colormap(jet) i.e. color picture.
Matlab code I use:
N = 4
FNAMEFMT = 'Frame%d.tif';
% Load images
for i=1:N
IMAGES = imread(sprintf(FNAMEFMT, i));
IMAGES = rgb2gray(IMAGES);
fname = sprintf('%s\\Frame%d.tif','C:\Project',i);
imagesc(IMAGES); axis image; colorbar; colormap(jet);
imwrite(IMAGES, fname, 'tif');
The pictures I import to MATLAB looking like that:
And I need to save them looking like that:
But the code I provided saves them again as black/white/gray.