This invention discloses a topical cooling compressive hemostasis and wound healing device and methods thereof for affecting a percutaneous access wound or an acute surgical wound where the device is compatible with physiological, circulatory and cellular microenvironments of the injury and conforming to the injury site anatomy. The device promotes hemostasis, sustains hemostasis and improves wound healing quality by controlling and affecting vasculature motions of the injury site during various wound healing phases. The device incorporates an elastic material compatible with the elastic nature of the injured vessel to promote comfort and safety. The elastic material is further thermally conductive to deliver and transport cooling and a therapeutic agent to the wound site. The device further incorporates an anatomically conforming lateral stabilization component to stabilize the injury sits and its surroundings.