The specific heat is calculated for a three-dimensional electron gas i
n metals under quantizing magnetic fields taking into account magnetic
interactions between conduction electrons (the Shoenberg effect). Und
er the conditions of the nonlinear de Haas-van Alphen (dHvA) effect th
e temperature jump in specific heat at a diamagnetic phase transition
is calculated. The jump occurring at the magnetic field corresponding
to the centre of the dHvA period is about of a few percent of the spec
ific heat in the absence of magnetic field. In gold and copper it is p
redicted to be larger than the maximal value of the change observed du
ring a.c. temperature measurements in heat capacity of beryllium in a
magnetic field. It is shown that the jump substantially increases with
increasing magnetic field. Limiting fields for existence of diamagnet
ic phase transitions at any temperature; as well as transition tempera
tures in gold and copper at certain fields, are estimated and it is fo
und that the latter coincide with the measured values.