We need … like … a bat signal.
Under the temporal method you use historical exchange rates for inventory and for COGS.
If you’re using FIFO, then the old costs go to COGS (so “historical” means historical: old costs, old exchange rates), and the new costs go to ending inventory (so “historical” means “new”: new costs, new exchange rates).
If you’re using LIFO, then the old costs go to ending inventory (so “historical” means historical: old costs, old exchange rates), and the new costs go to COGS (so “historical” means “new”: new costs, new exchange rates.)
The exception to these occurs when you buy and sell inventory (more or less) evenly throughout the year; in that case, “historical” means average: you use the (weighted) average exchange rate for the year.
If you’re using average cost for inventory and COGS, then “historical” means average; you use the (weighted) average exchange rate for the year.