Sure, I can help you generate a temporal profile for a hypothetical Purchase-to-Pay process. Here's an example temporal profile for a Purchase-to-Pay process where the average and standard deviation of the time between each couple of activities have been estimated based on industry benchmarks:
```python
purchase_to_pay_temporal_profile = {
    ('Create Purchase Requisition', 'Approve Purchase Requisition'): (1, 0.5), # In days
    ('Approve Purchase Requisition', 'Create Purchase Order'): (1, 0.5), # In days
    ('Create Purchase Order', 'Receive Goods'): (7, 2), # In days
    ('Receive Goods', 'Create Invoice'): (7, 2), # In days
    ('Create Invoice', 'Approve Invoice'): (3, 1), # In days
    ('Approve Invoice', 'Pay Invoice'): (7, 2), # In days
}
```
In this example, the temporal profile includes the following activity pairs and their corresponding average and standard deviation (in days):

* Creating a purchase requisition and approving it (1 day average, 0.5 day standard deviation)
* Approving a purchase requisition and creating a purchase order (1 day average, 0.5 day standard deviation)
* Creating a purchase order and receiving goods (7 days average, 2 day standard deviation)
* Receiving goods and creating an invoice (7 days average, 2 day standard deviation)
* Creating an invoice and approving it (3 days average, 1 day standard deviation)
* Approving an invoice and paying it (7 days average, 2 day standard deviation)

Note that these are just hypothetical estimates and may vary depending on the specific context and industry. Also, you may want to adjust the values based on your own analysis and data.