Sure, I can help you generate a hypothetical temporal profile for a Purchase-to-Pay process. The Purchase-to-Pay process typically involves the following activities: Purchase Request, Approval, Purchase Order, Delivery, Invoice Receipt, and Payment. Here's an example of a temporal profile:

```python
temporal_profile = {
    ('Purchase Request', 'Approval'): (24, 6),
    ('Approval', 'Purchase Order'): (48, 12),
    ('Purchase Order', 'Delivery'): (720, 144),
    ('Delivery', 'Invoice Receipt'): (48, 12),
    ('Invoice Receipt', 'Payment'): (24, 6),
    ('Purchase Request', 'Purchase Order'): (72, 18),
    ('Purchase Request', 'Delivery'): (744, 186),
    ('Purchase Request', 'Invoice Receipt'): (770, 198),
    ('Purchase Request', 'Payment'): (794, 208),
    ('Approval', 'Delivery'): (672, 168),
    ('Approval', 'Invoice Receipt'): (700, 175),
    ('Approval', 'Payment'): (724, 186),
    ('Purchase Order', 'Invoice Receipt'): (48, 12),
    ('Purchase Order', 'Payment'): (72, 18),
    ('Delivery', 'Payment'): (24, 6)
}
```

In this hypothetical profile, times are in hours. For example, the average time between 'Purchase Request' and 'Approval' is 24 hours, with a standard deviation of 6 hours. Similarly, the average time between 'Delivery' and 'Invoice Receipt' is 48 hours, with a standard deviation of 12 hours, and so on.

Please note that this is a hypothetical example and the actual times and standard deviations would depend on the specific characteristics of the process and the organization implementing it.