 Sure, I can generate a temporal profile for a hypothetical Purchase-to-Pay (P2P) process. Please note that the following temporal profile is just an example and the actual times between activities may vary based on the specifics of the process and the organization.

Here is a possible temporal profile for a P2P process:

```python
temporal_profile = {
    ('Purchase Request', 'Purchase Order'): (2, 1),
    ('Purchase Order', 'Goods Receipt'): (5, 1),
    ('Goods Receipt', 'Invoice Receipt'): (3, 0.5),
    ('Invoice Receipt', 'Invoice Verification'): (2, 1),
    ('Invoice Verification', 'Payment'): (5, 2),
}
```

This temporal profile shows the following average times and standard deviations between activities in the P2P process:

* The average time between Purchase Request and Purchase Order is 2 time units, with a standard deviation of 1 time unit.
* The average time between Purchase Order and Goods Receipt is 5 time units, with a standard deviation of 1 time unit.
* The average time between Goods Receipt and Invoice Receipt is 3 time units, with a standard deviation of 0.5 time units.
* The average time between Invoice Receipt and Invoice Verification is 2 time units, with a standard deviation of 1 time unit.
* The average time between Invoice Verification and Payment is 5 time units, with a standard deviation of 2 time units.

Again, these time units could be minutes, hours, days, or any other time measurement depending on the specifics of the P2P process and the organization.