You can use Newton's Law of Cooling to model both the heating and cooling of your valve. You'd use the data you already collected to establish the model, then use the model to see how long it takes the valve to approach equilibrium in the furnace. You can use the same model to estimate the temperature behavior between the time you removed the part from the furnace and when the Arduino was able to get a fix on the thermocouple.
Here's the detailed process for modeling the heating/cooling of the part. I'll be working with the following sample temperature ($T$) vs time ($t$) data. The data represents temperature data taken every minute, starting 5 minutes after the part is removed from the furnace.
t (min) T (C)
5 234
6 222
7 211
8 201
9 191
10 182
Take the natural logarithm of the temperature data, it should be roughly linear with respect to time. Now do a linear regression through $t$ vs. $ln(T)$ and you should get a slope ($\alpha$) and y-intercept of -0.05 and 5.704 respectively. I will post details on howused Excel to do the regression; LibreOffice Calc, Matlab, Octave, et al. should also do the job.
The temperature of the part just as it came out of the furnace ($T_0$) will be approximately equal to $e$ raised to the power of the y-intercept: $e^{5.704}$, or 300 C in this case.
You can use the slope and initial temperature from the linear fit combined with Newton's Law to model the cooling process:
$$ T(t)=T_0\cdot e^{\alpha t} $$
You can use the same equation to model the heating process in a little whilethe furnace by flipping the sign of $\alpha$, as long as the heat transfer modes within the furnace are similar to those during cooling, e.g. natural convection and radiation.