Twinx() を使用して副軸を持つプロットの凡例にラベルを追加するにはどうすればよいですか?

<code class="python">import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rc

time = np.arange(10)
temp = np.random.random(10)*30
Swdown = np.random.random(10)*100-10
Rn = np.random.random(10)*100-10

fig = plt.figure()
ax = fig.add_subplot(111)

lns1 = ax.plot(time, Swdown, '-', label = 'Swdown')
lns2 = ax.plot(time, Rn, '-', label = 'Rn')
ax2 = ax.twinx()
lns3 = ax2.plot(time, temp, '-r', label = 'temp')

# Add all lines and labels to a single legend
lns = lns1+lns2+lns3
labs = [l.get_label() for l in lns]
ax.legend(lns, labs, loc=0)

ax.grid()
ax.set_xlabel("Time (h)")
ax.set_ylabel(r"Radiation ($MJ\,m^{-2}\,d^{-1}$)")
ax2.set_ylabel(r"Temperature ($^\circ$C)")
ax2.set_ylim(0, 35)
ax.set_ylim(-20,100)
plt.show()</code>