You can actually observe most of the answer here on Earth. The key point is the heat conductivity of the Venusian rock is not very large. If the dense atmosphere was removed, the surface of Venus would be losing heat by radiating it into space. (It's also losing heat by convection into the atmosphere, but I believe that is a much smaller effect.) It is gaining heat by conduction from the bulk of Venus which is hot rock. As the surface cools, the rate of heat loss into space decreases and the rate of heat flow from the interior increases and the end-point temperature is where those two come into balance.
You can get a useful estimate of the time by considering the cooling of lava from a surface flow on Earth. We know that a flow only a few tens of feet thick will solidify entirely on the surface while the interior remains liquid (this is how lava tubes form), so we know that the lava is thick enough to be a good model for the much deeper hot rock on Venus.
A new lava flow cools to a solid surface within hours and is cool enough to walk on in days (provided no new lava underneath cracks the surface and allows new liquid lava out.) See this web page for some specifics.
This is a lower limit for the time needed on Venus, since atmospheric cooling is much more effective on Earth than it would be on Venus, but it points strongly to the time needed to cool to be safe to stand on being days to months and definitely less than years.