  Theoretically, materials that break multiple symmetries allow, under certain
conditions, the formation of four-fermion condensates above the superconducting
critical temperature. Such states can be stabilized by phase fluctuations.
Recently a fermionic quadrupling condensate that breaks the $Z_2$ time-reversal
symmetry was reported in Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ [V. Grinenko
et al., Nat. Phys. 17, 1254 (2021)]. Evidence for the new state of matter comes
from muon-spin rotation, transport, thermoelectric, and ultrasound experiments.
Observing a specific heat anomaly is a very important signature of a transition
to a new state of matter. However, a fluctuation-induced specific heat
singularity is usually very challenging to resolve from a background of other
contributions. Here, we report on detecting two anomalies in the specific heat
of Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ at zero magnetic field. The
anomaly at the higher temperature is accompanied by the appearance of a
spontaneous Nernst effect, indicating broken time-reversal ($Z_2$) symmetry.
The second anomaly at the lower temperature coincides with the transition to a
zero resistance state, indicating superconductivity breaking the $U(1)$ gauge
symmetry. Our data provide calorimetric evidence for the $Z_2$ phase formation
above the superconducting phase transition.
