The date on the battery seems to be 06/11? So it may just be suffering from old age.
Although the track has an uninterrupted supply there should be an IC inside the module to manage the charging and terminate it as necessary. A correct charging regime is important for longevity. Check out the NiMH stuff at BatteryUniversity.com
Edit: You may be right about temperature. 28C seems a bit too hot for a battery. Here's what the Fagerhult web-site says:-
"Since some emergency lighting components, for example batteries, are sensitive to temperature the physical solution varies for each luminaire. Some luminaires require the battery or both the battery and the emergency lighting electronics to be moved outside the luminaire and placed in a separate box (battery and emergency lighting box)."