T-stress　plays　an　important　role　in　the　fracture　of　various　materials,　and　is　frequently　adopted　as　a　second　fracture　parameter　in　addition　to　the　stress　intensity　factor.　In　this　paper,　the　T-stresses　for　cracks　in　both　homogeneous　and　functionally　graded　materials　under　thermal　loadings　are　computed　by　the　numerical　manifold　method　(NMM),　which　is　very　suitable　for　crack　modeling　due　to　the　use　of　bi-cover　systems.　After　the　calculation　of　temperature　and　displacement　fields　by　the　NMM　solver,　the　T-stress　is　extracted　through　the　domain-independent　interaction　integral.　The　proposed　method　is　verified　through　two　benchmark　problems　and　then　applied　to　study　three　more　complex　cases　where　the　effects　of　material　parameters　and　crack　configurations　on　the　T-stress　are　further　examined.　©　2021　Elsevier　Ltd