Previous　studies　have　suggested　a　crossover　from　superdiffusive　to　normal　heat　transport　in　one-dimensional　(1D)　anharmonic　oscillator　systems　with　a　double-well　type　interatomic　interaction　like　V(xi)　=　-xi(2)/2+　xi(4)/　4,　when　the　system　temperature　is　varied.　In　order　to　better　understand　this　unusual　manner　of　thermal　transport,　here　we　perform　a　direct　dynamics　simulation　to　examine　how　the　spreading　processes　of　the　three　physical　quantities,　i.　e.　the　heat,　the　total　energy　and　the　momentum,　would　depend　on　temperature.　We　find　three　main　points　that　are　worth　noting.　(i)　The　crossover　from　superdiffusive　to　normal　heat　transport　is　well　verified　from　a　new　perspective　of　heat　spread.　(ii)　The　spreading　of　the　total　energy　is　found　to　be　very　distinct　from　heat　diffusion,　especially　under　some　temperature　regimes,　energy　is　strongly　localized,　while　heat　can　be　superdi.　usive.　So　one　should　take　care　to　derive　a　general　connection　between　the　heat　conduction　and　energy　diffusion.　(iii)　In　a　narrow　range　of　temperatures,　the　spreading　of　momentum　implies　clear　unusual　non-ballistic　behaviors;　however,　such　unusual　transport　of　momentum　cannot　be　directly　related　to　the　normal　transport　of　heat.　An　analysis　of　phonon　spectra　suggests　that　one　should　also　take　the　effects　of　phonon　softening　into　account.　All　of　these　results　may　provide　insights　into　establishing　the　connection　between　the　macroscopic　heat　transport　and　the　underlying　dynamics　in　1D　systems.