 Creating a temporal profile for a hypothetical Purchase-to-Pay (P2P) process involves making assumptions about activity durations and their variability. Here's an example of a simplified temporal profile for a P2P process, where each key represents the pair of activities and values represent the average time (in seconds) and standard deviation (in seconds):

```python
temporal_profile = {
    ('Purchase Request', 'Purchase Order'): (3600, 180),  # Purchase Request -> Purchase Order: Average 1 hour, SD 3 minutes
    ('Purchase Order', 'Goods Received'): (7200, 900),   # Purchase Order -> Goods Received: Average 2 hours, SD 15 minutes
    ('Goods Received', 'Invoice Received'): (14400, 2880),  # Goods Received -> Invoice Received: Average 4 hours, SD 48 minutes
    ('Invoice Received', 'Purchase Invoice Approval'): (7200, 600),   # Invoice Received -> Purchase Invoice Approval: Average 2 hours, SD 10 minutes
    ('Purchase Invoice Approval', 'Payment Approval'): (14400, 3600),  # Purchase Invoice Approval -> Payment Approval: Average 4 hours, SD 1 hour
    ('Payment Approval', 'Payment'): (86400, 18000)   # Payment Approval -> Payment: Average 24 hours, SD 5 hours
}
```

This temporal profile assumes that each activity in the P2P process has some variability around an average time, and it's important to note that these numbers are just examples and may not reflect a real-world scenario. Additionally, the number of activities in this example (6) is also a simplification, as a real-world P2P process could involve many more stages.