EOL, you were very close..,
distance = [1,3,7,9]
energy = [10,20,30,40]
sigma = [1,3,2,5]
(_, caps, _) = plt.errorbar(distance, energy, sigma, capsize=20, elinewidth=3)
for cap in caps:
cap.set_color('red')
cap.set_markeredgewidth(10)
plt.show

set_markeredgewidth sets the width of the cap lines.
Matplotlib objects have so many attributes that often it is difficult to remember the right ones for a given object. IPython is a very useful tool for introspecting matplotlib. I used it to analyze the properties of the 2Dlines correponding to the error cap lines and I found that and other marker properties.
Cheers