Setting axes.linewidth without changing the rcParams global dict

• This answer does not work, as it is explained in the comments. I suggest using spines.
• As mentioned in a comment by Czechnology, consider changing the ticks too.

import matplotlib.pyplot as plt

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))

ax1.set_title('Normal spine and ticks')
ax2.set_title('Adjusted spine and ticks')

# change each spine separately:
# ax.spines['right'].set_linewidth(0.5)

# change all spines
for axis in ['top','bottom','left','right']:
    ax2.spines[axis].set_linewidth(4)

# increase tick width
ax2.tick_params(width=4)

plt.show()

• see more about spines at:
  • http://matplotlib.org/api/spines_api.html
  • http://matplotlib.org/examples/pylab_examples/multiple_yaxis_with_spines.html