Here's an example of a hypothetical temporal profile for a simplified Purchase-to-Pay (P2P) process. I've assumed certain average times and standard deviations between activities based on typical business processes. Note that these values can vary greatly depending on the organization, its size, industry, and other factors.

```python
p2p_temporal_profile = {
    ('Purchase Requisition', 'Purchase Order'): (7200, 1800),  # Avg: 2 hours, Std Dev: 30 minutes
    ('Purchase Order', 'Goods Received'): (259200, 43200),   # Avg: 3 days, Std Dev: 6 hours
    ('Goods Received', 'Invoice Received'): (10800, 7200),   # Avg: 3 hours, Std Dev: 2 hours
    ('Purchase Order', 'Invoice Received'): (432000, 86400), # Avg: 5 days, Std Dev: 1 day
    ('Goods Received', 'Three-Way Matching'): (172800, 36000), # Avg: 2 days, Std Dev: 6 hours
    ('Invoice Received', 'Three-Way Matching'): (10800, 5400), # Avg: 3 hours, Std Dev: 1.5 hours
    ('Three-Way Matching', 'Payment Processing'): (21600, 9000), # Avg: 6 hours, Std Dev: 2.5 hours
    ('Payment Processing', 'Payment Made'): (86400, 3600)   # Avg: 1 day, Std Dev: 1 hour
}
```

In this profile:

- Activities like 'Purchase Requisition' and 'Purchase Order' typically occur closely together.
- 'Goods Received' and 'Invoice Received' can happen near the same time or with a delay due to shipping times.
- 'Three-Way Matching' involves cross-checking purchase orders, invoices, and received goods, which usually takes some time but can vary based on process efficiency and workload.
- 'Payment Processing' might involve approvals, bank processing times, etc., adding variability to the time before a payment is made.