A thermally-conductive compound for forming a layer which is conformable between a first heat transfer surface (56; 82) located on a heat-generating source having an operating temperature range above normal room temperature and an opposing second heat transfer surface (54; 90) to provide a thermal pathway therebetween, the compound (30; 47) comprising an admixture of: (a) a matrix component; and (b) a first dispersed component forming first discrete domains within the matrix component, the compound (30; 47) having the following properties: the first discrete domains are form-stable at normal room temperature in a first phase and conformable between the first (56; 82) and second (54; 90) heat transfer surface in a second phase, the first discrete domains have a transition temperature above normal room temperature and within the operating temperature range of the heat-generating source from the first phase to the second phase, the matrix component is a thermal grease wherein the thermal grease comprises one or more oils selected from the group consisting of mineral oils, hydrocarbon oils, synthetic oils, and silicone oils, and combinations thereof, characterized in that the layer has a thickness (t 1) of 5 mils (125 μm) or less at room temperature under a given applied pressure of 6kPa or less, the thickness (t 1) of the layer decreases by at least 20% (t 2) under the given applied pressure within the operating temperature range of the heat-generating source when the heat-generating source is operated with the given applied pressure being applied; wherein the first dispersed component comprises one or more fusible metals, one or more fusible metal alloys, or a combination thereof; and wherein the one or more fusible metals or alloys comprises one or more of bismuth, tin, lead, cadmium, and indium. (a) a matrix component; and (b) a first dispersed component forming first discrete domains within the matrix component, the compound (30; 47) having the following properties: the first discrete domains are form-stable at normal room temperature in a first phase and conformable between the first (56; 82) and second (54; 90) heat transfer surface in a second phase, the first discrete domains have a transition temperature above normal room temperature and within the operating temperature range of the heat-generating source from the first phase to the second phase, the matrix component is a thermal grease wherein the thermal grease comprises one or more oils selected from the group consisting of mineral oils, hydrocarbon oils, synthetic oils, and silicone oils, and combinations thereof, characterized in that the layer has a thickness (t 1) of 5 mils (125 μm) or less at room temperature under a given applied pressure of 6kPa or less, the thickness (t 1) of the layer decreases by at least 20% (t 2) under the given applied pressure within the operating temperature range of the heat-generating source when the heat-generating source is operated with the given applied pressure being applied; wherein the first dispersed component comprises one or more fusible metals, one or more fusible metal alloys, or a combination thereof; and wherein the one or more fusible metals or alloys comprises one or more of bismuth, tin, lead, cadmium, and indium. the first discrete domains are form-stable at normal room temperature in a first phase and conformable between the first (56; 82) and second (54; 90) heat transfer surface in a second phase, the first discrete domains have a transition temperature above normal room temperature and within the operating temperature range of the heat-generating source from the first phase to the second phase, the matrix component is a thermal grease wherein the thermal grease comprises one or more oils selected from the group consisting of mineral oils, hydrocarbon oils, synthetic oils, and silicone oils, and combinations thereof, characterized in that the layer has a thickness (t 1) of 5 mils (125 μm) or less at room temperature under a given applied pressure of 6kPa or less, the thickness (t 1) of the layer decreases by at least 20% (t 2) under the given applied pressure within the operating temperature range of the heat-generating source when the heat-generating source is operated with the given applied pressure being applied; wherein the first dispersed component comprises one or more fusible metals, one or more fusible metal alloys, or a combination thereof; and wherein the one or more fusible metals or alloys comprises one or more of bismuth, tin, lead, cadmium, and indium.