The observed near-Earth-asteroid (NEA) population contains very few objects with small perihelion distances (q). NEAs that currently have orbits with relatively large q might have had a past evolution during which they have approached closer to the Sun. We present a probabilistic assessment of the minimum q that an asteroid with given orbital elements and absolute magnitude (H) has had at some point in its orbital history. At the same time, we offer an estimate of the time that it has spent having such an orbit. We have re-analyzed orbital integrations by Granvik et al. (2017,2018) of test asteroids from the moment they entered the near-Earth region (q≤1.3 AU) until they ended up in their respective sinks, such as a collision with the Sun or a planet, or an ejection from the inner regions of the Solar System. We considered a total disruption of asteroids at certain q as a function of H, as proposed in Granvik et al. (2016) in order for their NEO population model to match the observations. We calculated the probability that an asteroid with a given set of orbital elements (semi-major axis, eccentricity, inclination) and H has acquired a q value smaller than a given threshold value, as well as its respective dwell time in that range. We have constructed a look-up table containing this information that can be used in studies of the past orbital and thermal evolution of asteroids, as well as meteorite falls and their possible parent bodies.