  We present a mean-field theory describing the influence of long-range dipolar
forces on the temperature transition from the paramagnetic to ordered phases in
frustrated Heisenberg spiral magnets. It is shown that the dipolar interaction
produces a cascade of first- and second- order phase transitions between the
paramagnetic and the spiral states upon temperature decreasing. Depending on
system parameters, the following intermediate phases can arise: an
incommensurate and a commensurate sinusoidally modulated states, spiral phases
in which perpendicular spin components have different amplitudes and are
modulated with the same and with different wave vectors. We distinguish six
possible sequences of phase transitions upon temperature decreasing at least
four of which were observed before experimentally in specific compounds. It is
found that the action of dipolar forces cannot always be modeled even
qualitatively by small one-ion anisotropic spin interactions. We demonstrate
that the dipolar interaction is responsible for successive phase transitions in
the triangular-lattice multiferroic MnI$_2$: almost all available experimental
findings are described quantitatively within the mean-field theory by taking
into account the exchange, the dipolar and small symmetry-allowed anisotropic
spin interactions.
