  We extend the idea of fermion bags to Hamiltonian lattice field theories in
the continuous time formulation. Using a class of models we argue that the
temperature is a parameter that splits the fermion dynamics into small spatial
regions that can be used to identify fermion bags. Using this idea we construct
a continuous time quantum Monte Carlo algorithm and compute critical exponents
in the 3d Ising Gross-Neveu universality class using a single flavor of
massless Hamiltonian staggered fermions. We find $\eta$=0.54(6) and
$\nu$=0.88(2) using lattices up to N=2304 sites. We argue that even sizes up to
N=10,000 sites should be accessible with supercomputers available today.
