Yes, particles in a solid do have thermal energy, which is related to their vibrational motion. In solids, the particles (atoms or molecules) are closely packed together and held in fixed positions by strong intermolecular forces. While they cannot freely move around as they do in liquids and gases, they can still vibrate around their fixed positions.
Thermal energy in solids is associated with these vibrations, and this energy increases as the temperature of the solid rises. At absolute zero (0 Kelvin or -273.15°C), the vibrational motion of the particles theoretically comes to a stop, and the thermal energy is at its minimum. However, at any temperature above absolute zero, the particles will have some degree of thermal energy due to their vibrations.
It's important to note that while the thermal energy is present, solids retain their definite shape and volume because the particles are not free to move past one another like they would in a liquid or gaseous state.