  The observed near-Earth asteroid population contains very few objects with
small perihelion distances, say, q<=0.2 au. NEAs that currently have orbits
with larger q might be hiding a past evolution during which they have
approached closer to the Sun. We present a probabilistic assessment of the
minimum q that an asteroid has reached during its orbital history. At the same
time, we offer an estimate of the dwell time, that is, the time q has been in a
specific range. We have re-analyzed orbital integrations of test asteroids from
the moment they enter the near-Earth region until they either collide with a
major body or are thrown out from the inner Solar System. We considered a total
disruption of asteroids at certain q as a function of absolute magnitude (H).
We calculated the probability that an asteroid with given orbital elements and
H has reached a q smaller than a given threshold value and its respective dwell
time in that range. We have constructed a look-up table that can be used to
study the past orbital and thermal evolution of asteroids as well as meteorite
falls and their possible parent bodies. An application to 25 meteorite falls
shows that carbonaceous chondrites typically have short dwell times at small q,
whereas for ordinary chondrites it ranges from 10,000 to 500,000 years. A
dearth of meteorite falls with long dwell times and small minimum q supports a
super-catastrophic disruption of asteroids at small q.
