Nothing changes about the molecules when ice melts. Only their energy changes, and with it how tightly they can hold onto each other. Below is a real molecular-dynamics simulation: the particles attract each other weakly, repel hard when squeezed, and do whatever the temperature lets them.
Keep adding heat at a steady rate and the temperature does not rise steadily. Twice it stops completely: all the energy goes into breaking bonds rather than speeding molecules up. Those flat steps are latent heat, and they are why a pan of boiling water stays at 100 Β°C however high you turn the hob.
Live speed distribution from the simulation. The smooth line is the MaxwellβBoltzmann prediction β no particle was told to follow it; it falls out of random collisions.