Measurements by different workers have indicated that the friction coefficient &mgr; of a graphite brush contact decreases with rising contact temperatureT. IfP= mechanical load,Ab= load bearing area andF= friction force, the average pressure isp¯=P/Aband the specific friction force &psgr; =F/Ab. Hence &mgr; =F/P= &psgr;/p¯. It will be shown in this paper that the measured &mgr;(T) effect during smooth sliding is caused by the decrease of &psgr; with risingT.The specific friction force is a function of the character of the sliding surface alone, and &mgr; is, in addition, a function of the actual pressure inAb. It is shown that sliding, after a relatively short time, leads to a stage during whichAb, thus alsop¯, remains practically constant for more than 10 hr. The (&mgr;,T) test begins when such an ``initial stage,'' defined by &mgr;=&mgr;0,T=T0and constant contact voltageU, has been reached. It involvesTincreasing aboveT0and then decreasing toT0again, whereby the time of the test is short enough for constancy ofp¯. During a perfect (&mgr;,T) test, the forward and reversed curves agree with each other indicating thatAbhas remained constant.For all sliding stages with constantp¯, the relationship mentioned above can be written: &mgr;(T) = const&psgr;(T), which makes it possible to study &psgr; as a function ofTby studying &mgr; as a function ofT. The decrease of &psgr; with risingTis explained by assuming that adherence bonds inAbare broken or loosened byTaccording to a probability exp(−&phgr;/kT) = exp(−11600 &phgr;/T) with &phgr; in ev. The measured, strong dependence onTresults from the activation energy &phgr;=0.07 to 0.1 ev between the graphite ``platelets'' being of the order ofkT. Hence it is expected that &mgr; and &psgr; are inversely proportional to the probability factor. It was found that at constantAbup to about 500°K (the upper limit measured):&psgr;(T)&psgr;(T0)=&mgr;(T)&mgr;(T0)=exp11600[open pi]1T−1T0gives a very good agreement in the case of graphite members when the binding energy is assumed to be &phgr;=0.09 ev. For these contacts, &psgr; decreases from 0.12 to about 0.065 ton/cm2; simultaneously &mgr; decreases from 0.13 at 115°C to 0.07 at about 200°C. This has been found at atmospheric air pressure with dew point about 279°K and also in vacuum of 10−4mm Hg with dew point about 75°K. With a copper and gold ring at atmospheric air pressure, the (&mgr;,T) curves have a somewhat steeper slope and agreement with theory requires &psgr;=0.12 or 0.10 ev, respectively.At temperatures of about 500°K, &mgr; and &psgr; decrease very slowly and may reach a lower limit at temperatures when the chemisorbed gases on the graphite platelets begin to evaporate.