Heat Transfer / Conduction by free moving electrons

Free moving electrons near the heat Source gains KE and start to move rapidly along the solid and collides with distant particles and transfer the energy causing this distant particles to gain KE as so will vibrate more which increases its temperature.

1. By vibration of the particles which got transferred to neighbouring particles 

2. By free moving electron

So in metals the conduction happen in both ways so thats why its a good conductor