Continued growth of a single-walled carbon nanotube (SWNT) on an Fe cluster at 1500 K is demonstrated using quantum chemical molecular dynamics simulations based on the self-consistent-charge density-functional tight-binding (SCC-DFTB) method. In order to deal with charge transfer between carbon and metal particles and the multitude of electronic states, a finite electronic temperature approach is applied. We present trajectories of 45 ps length, where a continuous supply of carbon atoms is directed toward the C-Fe boundary between a 7.2 A long armchair (5,5) SWNT fragment and an attached Fe(38) cluster. The incident carbon atoms react readily at the C-Fe interface to form C- and C(2)-extensions on the tube rim that attach to the Fe cluster. These bridging sp-hybridized carbon fragments are vibrationally excited and highly mobile and, therefore, become engaged in frequent bond formation and breaking processes between their constituent C and the Fe atoms. The sp-hybridized carbon bridge dynamics and their reactions with the Fe-attached nanotube end bring about formations of new five-, six-, and seven-membered carbon rings extending the tube sidewall, resulting in overall continued growth of the nanotube on the Fe cluster up to nearly twice its length. Due to the random nature of new polygon formation, sidewall growth is observed as an irregular process without clear SWNT chirality preference. Compared to fullerene formation, heptagon formation is considerably promoted.