Here is a Python dictionary representing a temporal profile for a hypothetical Purchase-to-Pay process:
```python
temporal_profile = {
    ('Create Purchase Order', 'Approve Purchase Order'): (43200, 10800),  # 12 hours, 3 hours std dev
    ('Approve Purchase Order', 'Send Purchase Order to Supplier'): (21600, 3600),  # 6 hours, 1 hour std dev
    ('Send Purchase Order to Supplier', 'Receive Goods'): (604800, 86400),  # 7 days, 1 day std dev
    ('Receive Goods', 'Create Invoice'): (86400, 21600),  # 1 day, 6 hours std dev
    ('Create Invoice', 'Approve Invoice'): (43200, 10800),  # 12 hours, 3 hours std dev
    ('Approve Invoice', 'Pay Invoice'): (21600, 3600),  # 6 hours, 1 hour std dev
    ('Create Purchase Order', 'Receive Goods'): (864000, 172800),  # 10 days, 2 days std dev
    ('Create Purchase Order', 'Pay Invoice'): (1209600, 259200),  # 14 days, 3 days std dev
    ('Approve Purchase Order', 'Create Invoice'): (604800, 86400),  # 7 days, 1 day std dev
    ('Send Purchase Order to Supplier', 'Approve Invoice'): (864000, 172800),  # 10 days, 2 days std dev
}
```
This temporal profile models the average and standard deviation of the times between various activities in a Purchase-to-Pay process. The activities considered are:

1. Create Purchase Order
2. Approve Purchase Order
3. Send Purchase Order to Supplier
4. Receive Goods
5. Create Invoice
6. Approve Invoice
7. Pay Invoice

The profile assumes that the process typically takes around 10-14 days from creating a purchase order to paying the invoice. The standard deviations are set to reflect the variability in the process.

Note that this is a hypothetical example, and actual temporal profiles may vary depending on the specific organization and process.