Sure, here's an example of a temporal profile for an hypothetical Purchase-to-Pay process:
```python
temporal_profile = {
    ('Purchase Request', 'Purchase Order'): (86400, 3600), 
    ('Purchase Order', 'Order Approval'): (3600,900),
    ('Order Approval', 'Vendor Selection'): (14400, 1800),
    ('Vendor Selection', 'Purchase Requisition'): (28800, 3600),
    ('Purchase Requisition', 'Purchase Requisition Approval'): (3600, 1800),
    ('Purchase Requisition Approval', 'Purchase Order Creation'): (7200, 900),
    ('Purchase Order Creation', 'Vendor Acknowledgement'): (86400, 3600),
    ('Vendor Acknowledgement', 'Goods Receipt'): (120960, 7200),
    ('Goods Receipt', 'Invoice Receipt'): (172800, 14400),
    ('Invoice Receipt', 'Invoice Verification'): (14400, 1800),
    ('Invoice Verification', 'Invoice Posting'): (3600, 900),
    ('Invoice Posting', 'Payment Preparation'): (43200, 3600),
    ('Payment Preparation', 'Payment Execution'): (10800, 1800)
}
```

In this profile, the tuples represent activity pairs, and the numbers represent the time in seconds. For example, the average time between a `Purchase Request` and a `Purchase Order` is one day (86400 seconds) and the standard deviation is one hour (3600 seconds). Adjusting the values will depend on the context of the process and the characteristics of the organization that carries it out.