Thay was responsible (in a way) for the Dalek-Cyberman War as he was the one who made initial contact with the Cybermen whilst scouting. During their dialogue Thay was tricked into identiying himself and also insulted on his inelegant design, which made him a bit annoyed. (Judging by his remark of "DALEKS HAVE NO CONCEPT OF ELEGANCE!") So when the Cybermen proposed an alliance, he simply refused. After shrugging off the Cybermen's pathetic attacks he proceeded to blast them to oblivion. He escaped the battle with the other members of the Cult via an Emergency Temporal Shift, and arrived in 1930s New York via an Emergancy Temporal Shift.
Apart from sacrificing his lower panels to aid Sec's transformation into a hybrid, he did very little to prepare for the Final Experiment that the Cult of Skaro were planning, and instead went on scouting duty most of the time. The Cult were based in the sewers under New York so there were plenty of places to explore. He shared Dalek Caan's doubts about Dalek Sec's decision to transform the Dalek race into a bunch of softies, so like Dalek Caan he rebelled against Sec.
After taking Sec prisoner, Thay and Jast brought him and the Human Dalek Army to a theatre in New York to confront the Doctor. Thay boasted about how the Daleks would destroy and conquer and enslave and how awesome they were, but Dalek Sec simply remarked that death and destruction always turns against those who call it their allies. Dalek Thay refused to acknowledge this and was about to kill the Doctor when Sec got in the way of his shot and died.
Suprised, Thay decided to allow the Human-Daleks to kill the Doctor but they were angry with Thay for killing Sec. The Doctor explained that he had tampered with their DNA to make them less Dalek. Thay was disgusted by this and shot the nearest Hybrid, causing them all to fire on the two members of the Cult. Thay and Jast held their ground and slaughtered the front line of Human-Daleks, but being weaker due to his missing back panelling, Thay was quickly destroyed. Jast lasted a little longer but was annihilated soon afterwards.
Dalek Thay's Death, just before Dalek Jast, during a battle with the Dalek Humans.