The temporal profile for a hypothetical Purchase-to-Pay (P2P) process would depend on several factors such as the characteristics of the company's purchases and payments, its production cycles, order fulfillment processes, etc. However, I can provide you with an example of how to represent a typical P2P scenario based on those factors.

Assuming the following information:

* The average time between two orders (purchases) is 3 days.
* The average time between two payments (payments) is also 3 days.
* There are several production cycles in the process, and each cycle takes roughly 15 hours.
* The order fulfillment process may take an additional hour to complete per unit of production.

Let's create a temporal profile for this example:

```
temporal_profile = {
    ('Purchase', 'Production'): (3*24/7, 3*60) * 4, # assuming each production cycle takes 15 hours
    ('Payment', 'Production'): (3*24/7, 1.5),
}
```


This temporal profile represents the average time between two events in the P2P process: a production event and its related purchase or payment event.

Please note that this example is quite simplified for demonstration purposes. In real-world scenarios, the relationship between each pair of events would be more complex and specific to the business context.