A purchase-to-pay (P2P) process is a common business process involving several activities related to purchasing goods and services, such as issuing purchase orders, receiving goods, and processing payments. Here's an example of a temporal profile for an hypothetical Purchase-to-Pay process, represented as a Python dictionary:

```python
temporal_profile = {
    ('Initiate Purchase Order', 'Receive PO Approval"): (2 days, 12 hours),
    ('Receive PO Approval', 'Purchase Order Issued'): (1 day, 8 hours),
    ('Issue Purchase Order', 'Receive Item Delivery'): (2 weeks, 4 days),
    ('Receive Item Delivery', 'Inspect Items'): (1 day),
    ('Inspect Items', 'Create Receipt'): (3 days),
    ('Create Receipt', 'Process Invoice'): (1 day),
    ('Process Invoice', 'AP Team Review'): (2 days),
    ('AP Team Review', 'AP Team Approves Payment'): (1 day),
    ('AP Team Approves Payment', 'Payment Sent'): (2 days),
}
```

In this example, most of the temporal pairs are represented as tuples containing the average time (in days and hours) and the standard deviation (also in days and hours). This data might vary depending on the specific company's policies, industry norms, and operational efficiencies. The standard deviation reflects the resiliency of the process to variations while the average gives a sense of typical process duration. A lower standard deviation would mean that the process durations are more consistent, whereas a higher standard deviation might suggest more variability and potentially more risk or unpredictability in the process.