Seaborn is a high-level API for matplotlib, which takes care of a lot of the manual work.

seaborn.heatmap automatically plots a gradient at the side of the chart etc.

import numpy as np
import seaborn as sns
import matplotlib.pylab as plt

uniform_data = np.random.rand(10, 12)
ax = sns.heatmap(uniform_data, linewidth=0.5)
plt.show()

You can even plot upper / lower left / right triangles of square matrices. For example, a correlation matrix, which is square and is symmetric, so plotting all values would be redundant.

corr = np.corrcoef(np.random.randn(10, 200))
mask = np.zeros_like(corr)
mask[np.triu_indices_from(mask)] = True
with sns.axes_style("white"):
    ax = sns.heatmap(corr, mask=mask, vmax=.3, square=True,  cmap="YlGnBu")
    plt.show()

I'm late to the party, but here's a solution to OP's question using only matplotlib, as was requested. It relies on using imshow's extent option to do the job. For more info, see the matplotlib manual.

import matplotlib.pyplot as plt

xvals = [0,1]
yvals = [1,3]

zvals = [[0.6, 0.3, 0.2], [0.8, 0.4, 0.9]]

heatmap, ax = plt.subplots()

im = ax.imshow(zvals,cmap='inferno',extent=[xvals[0],xvals[1],yvals[0],yvals[1]],interpolation='nearest',origin='lower',aspect='auto')
ax.set(xlabel='some x', ylabel='some y')

cbar = heatmap.colorbar(im)
cbar.ax.set_ylabel('stuff')

heatmap.savefig('heatmap.png')

which results in the following image