Quite a busy one-liner, but here it is:

1. First ensure your NumPy array, myarray, is normalised with the max value at 1.0.
2. Apply the colormap directly to myarray.
3. Rescale to the 0-255 range.
4. Convert to integers, using np.uint8().
5. Use Image.fromarray().

And you're done:

from PIL import Image
from matplotlib import cm
im = Image.fromarray(np.uint8(cm.gist_earth(myarray)*255))

with plt.savefig():

with im.save():

You don't need to reshape. This is what rollaxis is for:

Image.fromarray(np.rollaxis(img, 0,3))

The RGB mode is expecting 8-bit values, so just casting your array should fix the problem:

In [25]: image = Image.fromarray(pixels.astype('uint8'), 'RGB')
    ...:
    ...: # Print out the pixel values
    ...: print image.getpixel((0, 0))
    ...: print image.getpixel((0, 1))
    ...: print image.getpixel((1, 0))
    ...: print image.getpixel((1, 1))
    ...:
(255, 0, 0)
(0, 0, 255)
(0, 255, 0)
(255, 255, 0)

In my comments I meant that you do something like this:

import numpy as np
from PIL import Image

img = np.array(image)
mean = 0
# var = 0.1
# sigma = var**0.5
gauss = np.random.normal(mean, 1, img.shape)

# normalize image to range [0,255]
noisy = img + gauss
minv = np.amin(noisy)
maxv = np.amax(noisy)
noisy = (255 * (noisy - minv) / (maxv - minv)).astype(np.uint8)

im = Image.fromarray(noisy)

Try specifying mode so that PIL is aware of data format.

img = Image.fromarray(source_array, mode="CMYK")

If that does not work, what is the shape of source array ?