  We study the superfluid transition of $^4$He in aerogel by Monte Carlo
simulations and finite size scaling analysis. Aerogel is a highly porous silica
glass, which we model by a diffusion limited cluster aggregation model. The
superfluid is modeled by a three dimensional XY model, with excluded bonds to
sites on the aerogel cluster. We obtain the correlation length exponent
$\nu=0.73 \pm 0.02$, in reasonable agreement with experiments and with previous
simulations. For the heat capacity exponent $\alpha$, both experiments and
previous simulations suggest deviations from the Josephson hyperscaling
relation $\alpha=2-d\nu$. In contrast, our Monte Carlo results support
hyperscaling with $\alpha= -0.2\pm 0.05$. We suggest a reinterpretation of
previous experiments, which avoids scaling violations and is consistent with
our simulation results.
