Take a metal disc and cut a small, circular hole in the center.
When you heat the whole thing, will the hole's diameter increase or decrease? and why?
What will happen to the diameter of disc?
[Physics] Will a hole cut into a metal disk expand or shrink when the disc is heated
material-sciencemetalstemperaturethermodynamics
Related Solutions
I think that mere touching does not bring the surfaces close enough. The surface of a metal is not perfect usually. Maybe it has an oxide layer that resists any kind of reaction. If the metal is extremely pure and if you bring two pieces of it extremely close together, then they will join together. It's also called cold welding.
For more information:
This module out of the University of Connecticut School of Engineering asks precisely "What are the thermal stresses resulting from an elevated temperature on a round beam fixed at both ends?" They use ANSI 1030, a low carbon steel, as an example material for the beam. Below is the setup (the steel beam fits snugly between two walls and then is heated up from room temperature):
Image source: University of Connecticut School of Engineering
The module gives the following equation for the thermal stress in the x-direction, $\sigma_x$:
$$\sigma_x = \alpha E \left(T - T_{ref}\right)$$
Using the values of $\alpha$, $E$, and $\left(T - T_{ref}\right)$ stated in the problem description, for this example $\sigma_x = 359.7\ MPa$. This is below the yield strength of ANSI 1030 steel, $441\ MPa$, so at this temperature it has not left the linear region of temperature vs. pressure.
Applying this to your own example: you will need to look up the $\alpha$ and $E$ for the specific metal, as these are material dependant constants. Those coupled with the final temperature of the rod vs. what it was before heating $\left(T - T_{ref}\right)$ will allow you to calculate the $\sigma_x$. As long as the $\sigma_x$ is below the yield strength of the material, it will remain in the linear region where the stress/pressure will depend linearly on the temperature of the bar.
Best Answer
Instead of a circular hole, let's think of a square hole. You can get a square hole two ways, you can cut it out of a complete sheet, or you can get one by cutting a sheet into 9 little squares and throwing away the center one. Since the 8 outer squares all get bigger when heat it, the inner square (the hole) also has to get bigger:
Same thing happens with a round hole.
This is confusing to people because the primary experience they have with stuff getting larger when heated is by cooking. If you leave a hole in the middle of a cookie and cook it, yes, the cookie gets bigger and the hole gets smaller. But the reason for this is that the cookie isn't so solid. It's more like a liquid, it's deforming. And as Ilmari Karonen points out, the cookie sheet isn't expanding much so there are frictional forces at work.