  We report low-temperature Raman signatures of the Heisenberg quantum magnet
Ca$_{10}$Cr$_7$O$_{28}$, showing clear anomalies in phonon mode frequencies and
linewidths below $\sim$100 K. This crossover temperature lies in between the
Jahn-Teller (JT) temperature scale ($>$ room temperature) and the temperature
scale associated with the spin exchange interactions ($<$ 12 K). Our
experimental observation is well captured by a novel secondary JT transition
associated with a cooperative reorientation of the orbitals giving rise to
anomalies in the temperature dependence of Raman frequencies and linewidths.
Such orbital reorganisation, in turn, affects the spin-spin exchange
interactions that decide the fate of the magnet at lower temperatures and hence
provide important clues to understand the energetics of the possible lower
temperature quantum paramagnetic phase.
