Depends on the upgrade type:
* For a proactive online upgrade I have no idea
* For a miles upgrade there will be no change apart from a possible small change in YQ
* For a cash upgrade to a regular higher cabin fare then the price of the upgrade may increase once various advance purchase thresholds are passed; for example if you buy a WTP ticket 50 days out the upgrade price to CW may be, say, GBP 1000 if I class is open, but if I class closes or you reach, say, a 21 day purchase limit for I the upgrade may go up to perhaps GBP 1500 as I and R fares may no longer be purchased; then perhaps 14 days in advance the price may go up to GBP 2,500 for a C fare and at 7 days the price might be GBP 3,500 to the full J fare.