Certainly! A Purchase-to-Pay (P2P) process, also known as a Procure-to-Pay process, typically involves a series of steps from purchasing goods to making payments. Below is a hypothetical temporal profile for a P2P process. Please note that the values for the average times and standard deviations are illustrative and can vary based on organization and context.

Here's a simplified version of a P2P process:

1. Create Purchase Requisition (PR)
2. Approve Purchase Requisition
3. Issue Purchase Order (PO)
4. Receive Goods/Services
5. Receive Invoice
6. Approve Invoice
7. Process Payment

Here is an example of a temporal profile with hypothetical average times and standard deviations for the series of activities:

```python
temporal_profile = {
    ('Create PR', 'Approve PR'): (4 * 60 * 60, 2 * 60 * 60), # 4 hours +/- 2 hours
    ('Create PR', 'Issue PO'): (24 * 60 * 60, 8 * 60 * 60), # 1 day +/- 8 hours
    ('Create PR', 'Receive Goods'): (5 * 24 * 60 * 60, 24 * 60 * 60), # 5 days +/- 1 day
    ('Approve PR', 'Issue PO'): (2 * 60 * 60, 1 * 60 * 60), # 2 hours +/- 1 hour
    ('Issue PO', 'Receive Goods'): (3 * 24 * 60 * 60, 24 * 60 * 60), # 3 days +/- 1 day
    ('Receive Goods', 'Receive Invoice'): (48 * 60 * 60, 8 * 60 * 60), # 2 days +/- 8 hours
    ('Receive Invoice', 'Approve Invoice'): (24 * 60 * 60, 4 * 60 * 60), # 1 day +/- 4 hours
    ('Approve Invoice', 'Process Payment'): (72 * 60 * 60, 16 * 60 * 60), # 3 days +/- 16 hours
    ('Issue PO', 'Receive Invoice'): (5 * 24 * 60 * 60, 48 * 60 * 60), # 5 days +/- 2 days
    ('Create PR', 'Receive Invoice'): (6 * 24 * 60 * 60, 48 * 60 * 60), # 6 days +/- 2 days
    ('Approve PR', 'Receive Invoice'): (5 * 24 * 60 * 60, 36 * 60 * 60), # 5 days +/- 1.5 days
    ('Create PR', 'Approve Invoice'): (7 * 24 * 60 * 60, 48 * 60 * 60), # 7 days +/- 2 days
    ('Approve PR', 'Approve Invoice'): (6 * 24 * 60 * 60, 36 * 60 * 60), # 6 days +/- 1.5 days
    ('Create PR', 'Process Payment'): (10 * 24 * 60 * 60, 72 * 60 * 60), # 10 days +/- 3 days
    ('Approve PR', 'Process Payment'): (9 * 24 * 60 * 60, 48 * 60 * 60), # 9 days +/- 2 days
    ('Issue PO', 'Process Payment'): (8 * 24 * 60 * 60, 48 * 60 * 60), # 8 days +/- 2 days
    ('Receive Goods', 'Process Payment'): (5 * 24 * 60 * 60, 36 * 60 * 60), # 5 days +/- 1.5 days
    ('Receive Invoice', 'Process Payment'): (3 * 24 * 60 * 60, 36 * 60 * 60), # 3 days +/- 1.5 days
}
```

In this profile, each key is a tuple representing a couple of activities, and its value is another tuple with the first element being the average time between the activities in seconds and the second one being the standard deviation, also in seconds. For instance, the average approval time for a Purchase Requisition is 4 hours with a standard deviation of 2 hours. 

This profile is hypothetical and would need to be derived from real-world data by analyzing the timestamps of process activities in a P2P execution log.