The process for creation of hot ice is called supersaturation.
Supersaturated solutions contain more dissolved solute than would normally exist in equilibrium so they exist in a meta-stable state, similar to that of a ball sitting at the apex of a steep mountain. As long as nothing happens to the solution, like the ball sitting precariously atop the mountain, it will continue on in that state. However, the slightest “nudge” in any direction and the supersaturated solution (and the ball) will try to restore itself to its most stable state by precipitating solute out of solution (or rolling down to the bottom of the mountain in the case of the ball).
When the Hot Ice solution is triggered (possibly by the addition of a seed crystal), the dissolved Sodium Acetate comes out of solution and returns to a solid form. During this transition, the solid Sodium Acetate (NaC2H3O2) absorbs 3 molecules of water into its crystal lattice, becoming Sodium Acetate Trihydrate (NaC2H3O2 ● 3 H2O). The process of hydration of Sodium Acetate is exothermic and heat is released during the transition, explaining why the Sodium Acetate crystals are warm even though the supersaturated solution was initially cold.
The chemical reaction can be written as:
NaC2H3O2 (s) + 3H2O (l) ---> NaC2H3O2 ● 3 H2O (s) + heat