This study provides an account of the bulk preparation of TlBa 2 Ca 2 Cu 3 O 9−δ (Tl-1223) superconductor at ambient pressure, and the critical temperature (T c ) features under thermalannealing conditions. The 'as-prepared' Tl-1223 (T c =106 K) presents a significantly higher T c =125 K after annealing the polycrystalline material in either flowing Ar+4% H 2 , or N 2 gases. In order to understand the fundamental reasons for a particular T c , we refined the average bulk structures using powder x-ray diffraction data. Although Ar+4%H 2 annealed Tl-1223 shows an increased 'c' lattice parameter, it shrinks by 0.03% (approximately unchanged) upon N 2 anneal. Due to such indeterminate conclusions on the average structural changes, local structures were investigated at using aberration-corrected scanning-transmission electron microscopy technique. Similar compositional changes in the atomic arrangements of both annealed-samples of Tl-1223 were detected in which the plane containing a Ca atomic layer gives a non-uniform contrast, due to substitution of some heavier Tl. In this report, extensive bulk properties are summarized through temperature-dependent resistivity, and shielding and Meissner fractions of magnetic susceptibility results; the bulk and local structures are investigated to correlate to properties.