An upside aluminium tray is placed directly over the flame on the blech and reaches yad soledes. Is one allowed to place a chalah on top of this tray in order to warm up the chalah.
Answer:
Some permit the reheating of cold and dry food that is fully cooked on top of an inverted pot. Although other authorities are stringent, requiring specifically a full pot of food, many are lenient to follow the former opinion. Therefore, it is permitted to heat a challah on top of the tray.
Sources: Concerning using an upside down tray/pot in general, see Shemiras Shabbos Kehilchasah note 112; Shevet Halevi 1:91; and see also https://dinonline.org/2011/02/03/shabbos-hatmana-returning-food-to-heat-on-shabbos/, note 12-13. Concerning heating a challah, see Yevakesh Torah, Shabbos, p. 172, who writes at length concerning whether one must be concerned for the hardening of the challah (and its becoming toast-like), and concludes that one may be lenient in this matter.