Here is an example of a temporal profile for a hypothetical Purchase-to-Pay process:

```
temporal_profile = {
    ('initiate_purchase', 'request_quote'): (43200, 21600),  # average: 12 hours, standard deviation: 6 hours
    ('request_quote', 'receive_quote'): (3600, 3600),  # average: 1 hour, standard deviation: 1 hour
    ('receive_quote', 'place_order'): (21600, 3600),  # average: 6 hours, standard deviation: 1 hour
    ('place_order', 'wait_for_delivery'): (43200, 21600),  # average: 12 hours, standard deviation: 6 hours
    ('wait_for_delivery', 'receive_delivery'): (21600, 3600),  # average: 6 hours, standard deviation: 1 hour
    ('receive_delivery', 'process_invoices'): (43200, 21600),  # average: 12 hours, standard deviation: 6 hours
    ('process_invoices', 'pay_provider'): (43200, 21600),  # average: 12 hours, standard deviation: 6 hours,
    ('pay_provider', 'close_transaction'): (3600, 3600),  # average: 1 hour, standard deviation: 1 hour
    ('close_transaction', 'postecute'): (43200, 21600)  # average: 12 hours, standard deviation: 6 hours
}
```

In this example, the temporal profile includes the average and standard deviation of the times between each couple of activities in the Purchase-to-Pay process. The times are given in seconds, and can be converted to hours or days if needed. Note that the values are just examples, in real-world scenarios the average and standard deviation times would be calculated based on actual data from the process.

Please note that for the sake of simplicity, the activities "initiate_purchase" and "postecute" are considered to be directly followed by the activity "request_quote" and "close_transaction" respectively.