You just need to have your values from the smallest to the largest :). This should not be a problem for you in another ben, but be careful with readers from the future, depth[indices]will throw TypeErrorif depth is a list instead of a numpy array!
>>> indices = np.argsort(depth)
>>> depth = depth[indices]
>>> temp = temp[indices]
>>> splrep(depth, temp)
(array([-7.05, -7.05, -7.05, -7.05, -5.03, -4.05, -3. , -2.01, -1.01,
1. , 1. , 1. , 1. ]), array([ 16.0147 , 15.54473241, 16.90606794, 14.55343229,
15.12525673, 14.0717599 , 15.19657895, 14.40437622,
14.7036 , 0. , 0. , 0. , 0. ]), 3)
Hat @FerdinandBeyer argsort "zip , zip, re-assign the values".