Resistivity non linear fit in Python

I'm trying to fit Einstein approximation of resistivity in a solid in a set of experimental data. I have resistivity vs temperature (from 200 to 4 K)

import xlrd as xd
import matplotlib.pyplot as plt
import numpy as np
import pylab as pl
import scipy as sp
from scipy.optimize import curve_fit

#retrieve data from file
data = pl.loadtxt('salita.txt')
Temp = data[:, 1]
Res = data[:, 2]

#define fitting function
def einstein_func( T, ro0, AE, TE):
    nl = np.sinh(TE/(2*T))
    return ro0 + AE*nl*T

p0 = sp.array([1 , 1, 1])

coeffs, cov = curve_fit(einstein_func, Temp, Res, p0)

But I get these warnings

crio.py:14: RuntimeWarning: divide by zero encountered in divide
  nl = np.sinh(TE/(2*T))
crio.py:14: RuntimeWarning: overflow encountered in sinh
  nl = np.sinh(TE/(2*T))
crio.py:15: RuntimeWarning: divide by zero encountered in divide
  return ro0 + AE*np.sinh(TE/(2*T))*T
crio.py:15: RuntimeWarning: overflow encountered in sinh
  return ro0 + AE*np.sinh(TE/(2*T))*T
crio.py:15: RuntimeWarning: invalid value encountered in multiply
  return ro0 + AE*np.sinh(TE/(2*T))*T
Traceback (most recent call last):
  File "crio.py", line 19, in <module>
    coeffs, cov = curve_fit(einstein_func, Temp, Res, p0)
  File "/System/Library/Frameworks/Python.framework/Versions/2.7/Extras/lib/python/scipy/optimize/minpack.py", line 511, in curve_fit
    raise RuntimeError(msg)
RuntimeError: Optimal parameters not found: Number of calls to function has reached maxfev = 800.

I don't understand why it keeps saying that there is a divide by zero in sinh, since I have strictly positive values. Varying my starting guess has no effect on it.

EDIT: My dataset is organized like this:

4.39531E+0  1.16083E-7
4.39555E+0  -5.92258E-8
4.39554E+0  -3.79045E-8
4.39525E+0  -2.13213E-8
4.39619E+0  -4.02736E-8
4.43130E+0  -1.42142E-8
4.45900E+0  -2.60594E-8
4.46129E+0  -9.00232E-8
4.46181E+0  1.42142E-7
4.46195E+0  -2.13213E-8
4.46225E+0  4.26426E-8
4.46864E+0  -2.60594E-8
4.47628E+0  1.37404E-7
4.47747E+0  9.47612E-9
4.48008E+0  2.84284E-8
4.48795E+0  1.35035E-7
4.49804E+0  1.39773E-7
4.51151E+0  -1.75308E-7
4.54916E+0  -1.63463E-7
4.59176E+0  -2.36902E-9

where the first column is temperature and the second one is resistivity (negative values are due to noise in trial current since the sample is a PbIn alloy which becomes superconductive at temperature lower than 6.7-6.9K, here we are at 4.5K).

Argument I'm providing to sinh are Numpy arrays, with a linear function ro0 + AE*T my code works. I've tried with scipy.optimize.minimize but the result is the same. Now I see that I have almost nine hundred values in my file, may that be the problem?

I have edited my dataset removing some lines and now the only warning showing is

RuntimeWarning: overflow encountered in sinh

How can I workaround it?

Solution

Here are a couple of observations that could help:

You could try the least-squares fit directly with leastsq, providing the Jacobian, which might help tame it.
I'm guessing you don't want the superconducting temperatures in your data set at all if you're fitting to an Einstein model (do you have a source for this eqn, btw?)
Do make sure your initial guesses are as good as they could possibly be (ro0=AE=TE=1 probably won't cut it).
Plot your data and make sure there aren't any weird artefacts
You seem to be indexing your data array in the wrong way in your code example: if the data is structured as you say, you want:

Temp = data[:, 0] Res = data[:, 1]

(Python indexes start at 0).