1. The temperature of the wort is the principal factor that will affect oil extraction from hops
2. Once the hops are separated from the wort, what has been extracted from the hops will no longer change
(3)* will the slow cooling of a cube continue to affect whatever hop oils etc. has been extracted?
1. Yes and no: it's complicated.
2. Not so: it will continue to change
There are five* things going on simultaneously: extraction of alpha acids, isomerisation of the alpha acids to the bitter iso alpha acids (IAA), degradation of the iso alpha acids to less bitter compounds, extraction of flavour compounds other than alpha acids and volatilisation (loss) of these flavour compounds.
The two extraction steps (1 and 4 above) are both included in extraction from hops. I do not know of any studies that give accurate estimates of the extraction rates involved, presumably because they are highly variable with things like lupulin gland size and structure, degree of rupture during processing and the activity of contact surfaces. If you've ever rubbed a fresh hop in your hand you'll know that the resins are released quite quickly and that they stick to everything.
Two further complications arise: the resinous material (AKA hop oils) can be released into the wort without dissolving (sometimes it's visible as oily spots) and since all hop components are poorly soluble but IAAs are more soluble than AAs, some of step 1 occurs after step 2 eg the alpha acids are isomerised in situ then the IAAs formed dissolve into the wort. This effect is exploited in pre-isomerised hop pellets.
All of these processes are influenced by temperature but only the temperature effect on steps 2 and 3 are well characterised. The extraction rates are also influenced by the boil vigour, stirring (if present) and such things as passage through a calandria.
It follows from the above that wort drawn from the kettle will have alpha acids that aren't yet isomerised entrained in it and further exposure to heat will transform these to IAAs, increasing the bitterness. This includes slow cooling time in the cube.
* Actually there are lots of other things going on at once but these are the five that concern us here.