The theory and procedure are described in this paper:  J. Brody and M. Brown, Am. J. Phys. 85, 582 (2017) https://doi.org/10.1119/1.4983649

You can download the Arduino software here and the latest version of Python (3.6?) here.  Then, the pyserial library has to be installed separately by opening the Anaconda Prompt (as administrator, if it gives you that option) and typing  "conda install pyserial".  To be able to generate real-time plots, open Spyder (installed with Anaconda).  Under the Tools menu, select Preferences.  Highlight IPython console, then select the Graphics tab.  Set the Graphics backend to Automatic.

If you have a single temperature sensor, use this Arduino sketch and this Python script.

If you have three temperature sensors at different positions on a rod, use this Arduino sketch and this Python script.

How to wire the TMP36GT9Z sensor to the Arduino:  Here's the data sheet.  The middle pin is wired to one of the Arduino analog inputs (use A0 if you have one sensor; use A0, A1, and A2 if you have three sensors).  The other two pins are ground and 5 V (both provided by the Arduino).  CAUTION:  It's extremely important not to reverse these two pins, or the sensor will get very hot and burn your fingers!  

How to use the Arduino sketches:  Plug in the Arduino UNO.  Go to the Start menu (or equivalent) and find the Arduino in the list of Devices and Printers.  Note the "COM" port number of the Arduino.  Open the Arduino software.  Under Tools, select the appropriate Port number.  Open and upload the Arduino sketch.  When it's running on the Arduino board, the TX LED will flash every 5 s.  You can open the Serial Monitor to view the data (time in milliseconds and temperature in Celsius).  Close the Serial Monitor before running the Python script.

How to use the Python scripts:  Open Spyder to run the scripts.  There are a lot of parameters you may need to change (all material parameters are in mks units):  

• "ta" is ambient temperature in Celsius.  (The sensors have a precision of about 0.1 degree, but an accuracy as poor as +/- 3 degrees.  To calibrate the sensors, the script adjusts temperatures such that initial adjusted temperature is ambient temperature.)
• "minutes" is how long you want to take data.  For sensors within an inch of the bottom of the rod, 10 minutes is plenty.  Higher up the rod, 15 or more minutes may be necessary to reach steady-state or even to see signficant cooling.
• a=serial.Serial('COM12',9600) must be changed to specify the correct port number of the Arduino.
• x1, x2, and x3 are the distances of the sensors from the bottom of the rod.
• l is the length of the rod.
• p is the perimeter of the rod, calculated by default from the width (called "side"), assuming square cross section.
• a is the cross sectional area, calculated by default from the width, assuming square cross section.
• rho is the density of the rod, which you can measure or look up for the material.
• c is the specific heat, which you can estimate by looking up typical values for the material.
• terms is the number of terms in the truncated infinite series.  I often find that 10 is adequate. 

Open an IPython console.  Start running the Python script at the same time you immerse the bottom of the rod in ice water.  (time=0 has to be the instant the rod contacts the ice water.)  A real-time plot of the data should appear in a separate window.  When the data acquisition is complete, fitted theoretical curves will appear in the figure (you may need to zoom in to see them if the fits are really good), and the fitting parameters (alpha, m, and h0) will be shown in the console.  If the data looks decent but the fit fails, you can try adjusting the bounds and initial guesses for the fitting parameters.  

If you have data in Excel, you can import it into Python and fit it with this script.

If you have any questions or suggestions, please don't hesistate to email me.