Yes, under certain conditions, a metal rod can indeed glow blue when heated to a specific temperature. The phenomenon you're referring to is known as incandescence.
When a metal is heated, its temperature gradually increases. As the temperature rises, the atoms or ions within the metal gain thermal energy, causing them to vibrate more vigorously. Eventually, if the temperature reaches a certain threshold, the metal will begin to emit visible light.
The color of the emitted light depends on the temperature of the metal. At lower temperatures, the light emitted appears red, and as the temperature increases, the color shifts towards orange, yellow, and eventually blue. At very high temperatures, the metal can even emit white light.
The color emitted by a heated metal is related to the distribution of energy among the electrons in the metal's atoms. When atoms absorb energy, their electrons move to higher energy levels. As the electrons return to their original energy levels, they release energy in the form of light. The specific energy levels involved determine the wavelength and, consequently, the color of the emitted light.
It's worth noting that the temperature required for a metal to glow blue varies depending on the metal itself. Different metals have different melting points and different temperature-color relationships. So while it's hypothetically possible for a metal rod to glow blue without melting or evaporating, the specific temperature required would depend on the properties of the metal in question.