A polymer that is capable of affording a heat storage material superior in humidity permeability and shape retention after phase transition and that is superior in molding processability is provided. The polymer includes constitutional units (A) derived from ethylene, constitutional units (B) represented by a specified formula, and optionally includes constitutional units (C) represented by another specified formula. Where the total number of the units (A), the units (B), and the units (C) is 100%, the number of the units (A) accounts for 70% to 99%, the total number of the units (B) and the units (C) accounts for 1% by weight to 30% by weight. Where the total number of the units (B) and the units (C) is 100%, the number of the units (B) accounts for 1% to 100% and the number of the units (C) accounts for 0% to 99%.