Shilajt, according to Tibetan Medicine, is cooling and balancing, and is used to remove heat. It can be used as a chulen, and it is present in many medicines since it enhances their effects. It is especially good for removing heat in liver and gall bladder.
It is true that some in Ayurveda considers it to be warming, etc. However, in the treatise Astangha Hridaya it asserts that the taste of shilajit is bitter, and that it's effect is "not very hot", but its post-digestive effect is hot.
So there there some slight differences in how this herb is understood, but in the main, the two systems are not really far apart in how the prepare and use this substance.
འ༔ ཨ༔ ཧ༔ ཤ༔ ས༔ མ༔Though there are infinite liberating gateways of Dharma,
there are none not included in the dimension of the knowledge of the Great Perfection.
-- Buddha Samantabhadri