We used local thermal analysis and ellipsometry to measure the glass transition temperatures (T-g) of supported thin films of poly(4-hydroxystyrene) (PHS) and hydroxy terminated polystyrene (PS-OH). The films were spuncast from solution onto silicon oxide substrates and annealed under vacuum at elevated temperatures to graft the polymer to the substrate. Grafting was verified and characterized in terms of the thickness of and the advancing contact angle of water on the residual layer after solvent extraction. For PHS, each segment of the polymer chain was capable of grafting to the substrate. The thickness of the residual layer increased with increasing annealing temperature. For this polymer the critical thickness below which the T-g of the film deviated from the bulk value was nearly 200 nm after annealing at the highest temperature (190 degreesC); the T-g of films 100 nm thick or less were elevated by more than 50 degreesC above the bulk value. For PS-OH films the polymer was only capable of grafting at one chain end, forming a brush layer at the substrate interface. The critical thicknesses for PS-OH films and the T-g elevations were substantially higher than for ungrafted PS films, but were not as large as for PHS. The film thickness dependence of T-g for PHS and PS-OH were well described as piecewise linear, consistent with a "dual-mechanism" model.