Certainly! The "Purchase-to-Pay" (P2P) process refers to the common series of activities that occur from purchasing goods or services through payment. Here's a hypothetical temporal profile based on common activities typically found in this process:

```
Temporal Profile for Purchase-to-Pay Process

{
    ('Order Creation', 'Invoice Receiving'): (86400, 21600),   # Time between creating an order and receiving the invoice
    ('Invoice Receiving', 'Invoice Processing'): (3600, 720),     # Time after receiving the invoice until it's processed
    ('Invoice Processing', 'Vendor Payment Request'): (86400, 10800), # Time to request payment after processing an invoice
    ('Vendor Payment Request', 'Payment Confirmation'): (3600, 900),   # Waiting for confirmation from the vendor's bank 
    ('Payment Confirmation', 'Invoice Archiving'): (259200, 172800), # Time from receiving payment confirmation to archiving the invoice
}
```

In this temporal profile:

- The time between creating an order and receiving the invoice is typically one day, with a standard deviation of six hours.
- After receiving the invoice, it takes approximately an hour for processing, with a standard deviation of 1.2 hours before proceeding to request payment.
- It can take up to 24 hours (one day) after processing to request payment with a standard deviation of three hours.
- There is typically a one-hour wait from when payment confirmation is received until the invoice can be archived, with a standard deviation of 30 minutes. 

Remember that these times and their variability should be customized based on actual company procedures and processes.

This profile provides an average time (in seconds) between each couple of activities as well as its standard deviation.