The BJT collector current equation is
$$i_C = I_S\cdot e^{\frac{v_{BE}}{V_T}}\left(1 + \frac{v_{CB}}{V_A}\right)$$
where \$V_A\$ is the Early voltage. But, this formula is often written as
$$i_C = I_S\cdot e^{\frac{v_{BE}}{V_T}}\left(1 + \frac{v_{CE}}{V_A}\right)$$
Thus
$$\frac{\partial i_C}{\partial v_{CE}} = \frac{I_S\cdot e^{\frac{V_{BE}}{V_T}}}{V_A} = \frac{i_C}{V_A + v_{CE}}$$
This is clearly a non-linear function of the collector-emitter voltage and collector current so this cannot be interpreted as a conductance.
However, for small changes around some fixed value of collector current \$I_C\$ and collector-emitter voltage \$V_{CE}\$, we can write
$$I_C + i_c \approx I_C\left(1 + \frac{v_{ce}}{V_A + V_{CE}} \right) = I_C + \frac{v_{ce}}{r_o}$$
where
$$r_o = \frac{V_A + V_{CE}}{I_C}$$
We call \$r_o\$ the collector-emitter dynamic, or differential or small-signal resistance.
It is not a true resistance since it is not constant but, instead, varies with the operating point of the transistor as can be seen by the formula.
Your very first equation is wrong. If you check your link, it should be
Vbe = (kT/q) ln(ic/is)
When you correct your math, the temperature for your circuit is just about 300 K. Actually, assuming a current ratio of 100 gives 302.45 K, but that isn't quite right, and I'm too lazy to solve for the exact values. Plus, I doubt that your experimental error would support any more precision.
And, just as bit of advice, when you are working with measurements which have 3 significant digits, reporting a computation to 16 significant digits suggests very strongly that you have no idea what the limitations of your measurements are. Just a tip.
Best Answer
You can measure the voltage between any two points. For example, I could measure \$V_{kitchensink,tongue}\$ like this:
While this is probably not a meaningful measurement, it is defined anyway, because my tongue exists at some electric potential, and my kitchen sink exists at some other electric potential, and the difference between them is the "voltage", which is more accurately called the electric potential difference.