If you want the image at the corner of your actual figure (rather than the corner of your axis), look into figimage.

Perhaps something like this? (using PIL to read the image):

import matplotlib.pyplot as plt
import Image
import numpy as np

im = Image.open('/home/jofer/logo.png')
height = im.size[1]

# We need a float array between 0-1, rather than
# a uint8 array between 0-255
im = np.array(im).astype(np.float) / 255

fig = plt.figure()

plt.plot(np.arange(10), 4 * np.arange(10))

# With newer (1.0) versions of matplotlib, you can 
# use the "zorder" kwarg to make the image overlay
# the plot, rather than hide behind it... (e.g. zorder=10)
fig.figimage(im, 0, fig.bbox.ymax - height)

# (Saving with the same dpi as the screen default to
#  avoid displacing the logo image)
fig.savefig('/home/jofer/temp.png', dpi=80)

plt.show()

Another option, if you'd like to have the image be a fixed fraction of the figure's width/height is to create a "dummy" axes and place the image in it with imshow. This way the image's size and position is independent of DPI and the figure's absolute size:

import matplotlib.pyplot as plt
from matplotlib.cbook import get_sample_data

im = plt.imread(get_sample_data('grace_hopper.jpg'))

fig, ax = plt.subplots()
ax.plot(range(10))

# Place the image in the upper-right corner of the figure
#--------------------------------------------------------
# We're specifying the position and size in _figure_ coordinates, so the image
# will shrink/grow as the figure is resized. Remove "zorder=-1" to place the
# image in front of the axes.
newax = fig.add_axes([0.8, 0.8, 0.2, 0.2], anchor='NE', zorder=-1)
newax.imshow(im)
newax.axis('off')

plt.show()

You are calling both subplots, which, by default, gives you a single axes, and also adding axes via add_axes. You should do one or the other, e.g.

...
fig = plt.figure()
ht_ax = fig.add_axes([0.1, 0.1, 0.3, 0.8])
cb_ax = fig.add_axes([0.45, 0.3, 0.02, 0.4])
phyl_ax = fig.add_axes([0.6, 0.1, 0.3, 0.8])

...

--or--

...
fig, ax = plt.subplots(1,2)
fig.subplots_adjust(left=0.15)
ht_ax = ax[0]
phyl_ax = ax[1]
cb_ax=fig.add_axes([0.05, 0.3, 0.02, 0.4])

...

You can use subplots_adjust and set_aspect to adjust the layout. You can also use colorbar.make_axes to get an appropriately sized colorbar axes. Here I also used grid_spec to get the plots to be a size ratio I liked

gs = gridspec.GridSpec(1, 2, width_ratios=[3, 2]) 
ht_ax = plt.subplot(gs[0])
phyl_ax = plt.subplot(gs[1])
cb_ax, kw = mpl.colorbar.make_axes(ht_ax, shrink=0.55)
...
cb = mpl.colorbar.ColorbarBase(ax=cb_ax, cmap=cmap, norm=norm, extend='both', **kw)

This demo from the matplotlib gallery shows how to insert pictures, draw lines to them, etc. I'll post the image from the gallery, and you can follow the link to see the code.

And here's the code (from version 2.1.2):

import matplotlib.pyplot as plt
import numpy as np

from matplotlib.patches import Circle
from matplotlib.offsetbox import (TextArea, DrawingArea, OffsetImage,
                                  AnnotationBbox)
from matplotlib.cbook import get_sample_data


if 1:
    fig, ax = plt.subplots()

    # Define a 1st position to annotate (display it with a marker)
    xy = (0.5, 0.7)
    ax.plot(xy[0], xy[1], ".r")

    # Annotate the 1st position with a text box ('Test 1')
    offsetbox = TextArea("Test 1", minimumdescent=False)

    ab = AnnotationBbox(offsetbox, xy,
                        xybox=(-20, 40),
                        xycoords='data',
                        boxcoords="offset points",
                        arrowprops=dict(arrowstyle="->"))
    ax.add_artist(ab)

    # Annotate the 1st position with another text box ('Test')
    offsetbox = TextArea("Test", minimumdescent=False)

    ab = AnnotationBbox(offsetbox, xy,
                        xybox=(1.02, xy[1]),
                        xycoords='data',
                        boxcoords=("axes fraction", "data"),
                        box_alignment=(0., 0.5),
                        arrowprops=dict(arrowstyle="->"))
    ax.add_artist(ab)

    # Define a 2nd position to annotate (don't display with a marker this time)
    xy = [0.3, 0.55]

    # Annotate the 2nd position with a circle patch
    da = DrawingArea(20, 20, 0, 0)
    p = Circle((10, 10), 10)
    da.add_artist(p)

    ab = AnnotationBbox(da, xy,
                        xybox=(1.02, xy[1]),
                        xycoords='data',
                        boxcoords=("axes fraction", "data"),
                        box_alignment=(0., 0.5),
                        arrowprops=dict(arrowstyle="->"))

    ax.add_artist(ab)

    # Annotate the 2nd position with an image (a generated array of pixels)
    arr = np.arange(100).reshape((10, 10))
    im = OffsetImage(arr, zoom=2)
    im.image.axes = ax

    ab = AnnotationBbox(im, xy,
                        xybox=(-50., 50.),
                        xycoords='data',
                        boxcoords="offset points",
                        pad=0.3,
                        arrowprops=dict(arrowstyle="->"))

    ax.add_artist(ab)

    # Annotate the 2nd position with another image (a Grace Hopper portrait)
    fn = get_sample_data("grace_hopper.png", asfileobj=False)
    arr_img = plt.imread(fn, format='png')

    imagebox = OffsetImage(arr_img, zoom=0.2)
    imagebox.image.axes = ax

    ab = AnnotationBbox(imagebox, xy,
                        xybox=(120., -80.),
                        xycoords='data',
                        boxcoords="offset points",
                        pad=0.5,
                        arrowprops=dict(
                            arrowstyle="->",
                            connectionstyle="angle,angleA=0,angleB=90,rad=3")
                        )

    ax.add_artist(ab)

    # Fix the display limits to see everything
    ax.set_xlim(0, 1)
    ax.set_ylim(0, 1)

    plt.show()