Spectroscopic studies are carried out on the cyclotron emission from the hot spots of $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ two-dimensional electron gas systems in a quantum Hall regime at $B=6.0\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ $(\ensuremath{\nu}=2.5)$ and $7.5\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ $(\ensuremath{\nu}=2.0)$ at $T=4.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ by applying a terahertz scanning microscope. The spectra at the current entry and exit corners (hot spots) are remarkably broadened towards lower frequencies with increasing $I$ up to $300\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{A}$, indicating the significant relevance of higher excited Landau levels. The spectra are analyzed by assuming that the effective electron temperature, ${T}_{E}$, at the local injection/withdrawal point reaches a maximum $\ensuremath{\sim}300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ while it is ${T}_{E}=25--30\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ when averaged over the region determined by the spatial resolution ($50\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ diameter).