Microstructural modification of high temperature superconductor (HTS) single-crystal plates of T1-1212 and T1-2212 (numbers designate the Tl/Ba/Ca/Cu cation ratio) was studied during 1.5 MeV Kr+ and Xe+ ion irradiation with in-situ electron diffraction and after ion irradiation with high resolution TEM (HRTEM). Similar in-situ temperature dependence effects are seen for both phases. During irradiations from 22K to 673K, an amorphous halo develops after very low ion dose or fluence (l.7X1012 ions/cm2). During irradiation at 100K and 300K, complete amorphization is obtained, while at 22K and ≥533K, the halo fades slightly and a polycrystalline ring pattern develops, indicating ion irradiation induced crystallization occurred. After a low ion dose (8.5XlO12ions/cm2) at 100K and 300K, HRTEM reveals amorphous regions 5 -20 nm in size which are not columnar and do not all penetrate the entire sample thickness. At 22K and ≥533K, Moire fringes and misoriented crystallites of cascade size are observed. The 4 - 6nm crystallites are thallium-rich.