A highly thermally conductive but yet highly conformable composition is made from gel filled with alumina. The use of .alpha.-alumina in which at least 10 weight % of the .alpha.-alumina particles have a particle size of at least 74 .mu.m makes possible the high filler levels needed to attain high thermal conductivity, without causing the decrease in elongation and softness normally associated with high filler levels. Further improvements are observed if the .alpha.-alumina and the gel (or precursor thereof) are mixed with a specific energy input of at least 10 Joule/g. The input of such specific energy has the effect making the resulting composition more conformable than it otherwise would be. The composition may be internally supported by a flexible matrix such as a fabric or open-celled foam.