  Temperley's bijection relates the toroidal dimer model to cycle rooted
spanning forests ($CRSF$) on the torus. The height function of the dimer model
and the homology class of $CRSF$ are naturally related. When the size of the
torus tends to infinity, we show that the measure on $CRSF$ arising from the
dimer model converges to a measure on (disconnected) spanning forests or
spanning trees. There is a phase transition, which is determined by the average
height change.
