the hand that has finally , to some extent , warmed up to him 
(ROOT (NP (NP (DT the) (NN hand)) (SBAR (WHNP (WDT that)) (S (VP (VBZ has) (ADVP (RB finally)) (, ,) (PP (IN to) (NP (DT some) (NN extent))) (, ,) (VP (VBD warmed) (PRT (RP up)) (PP (IN to) (NP (PRP him)))))))))
(ROOT (NP (NP (DT ) (NN )) (SBAR (WHNP (WDT )) (S (VP (VBZ ) (ADVP (RB )) (, ) (PP (IN ) (NP (DT ) (NN ))) (, ) (VP (VBD ) (PRT (RP )) (PP (IN ) (NP (PRP )))))))))