Sure, a hypothetical temporal profile for a Purchase-to-Pay process might look something like this:

```python
purchase_to_pay_temporal_profile = {('Choose Supplier', 'Order Goods'): (7200, 3600),
                                    ('Order Goods', 'Goods Delivered'): (86400, 14400),
                                    ('Goods Delivered', 'Check Invoice'): (18000, 3600),
                                    ('Check Invoice', 'Authorize Payment'): (3600, 1800),
                                    ('Authorize Payment', 'Pay Invoice'): (7200, 1800)}
```

This indicates the following:
- The average time between choosing a supplier and ordering goods is 2 hours, with a standard deviation of 1 hour.
- The average time between ordering goods and the goods being delivered is 1 day, with a standard deviation of 4 hours.
- The average time between the goods being delivered and checking the invoice is 5 hours, with a standard deviation of 1 hour.
- The average time between checking the invoice and authorizing the payment is 1 hour, with a standard deviation of 30 minutes.
- The average time between authorizing the payment and paying the invoice is 2 hours, with a standard deviation of 30 minutes.