Rule to calculate pump filtration time depending on temperature

Your explanations belie some fundamental misunderstandings about how Rules work.

postUpdate is one way to set the state of Items. That is all. Variables are set using =.

If you want to set a variable that keeps it’s value across multiple runs off the rule or across multiple different rules the variable needs to be declared as a global.

Presumably as a global? Otherwise this rule would not be able to use it.

Using intValue had nothing to do with whether a variable can be used in other rules. Where you declare it (i.e. within the Rule it as a global) controls that.

=

First of all, you can’t send an Item in a postUpdate. You must use

temperature_updated.postUpdate(temperature_pool.state)

To answer your question, eventually you will want to do something like Design Pattern: Associated Items. But I would recommend waiting until you are a bit more comfortable with some of the Rules DSL basics first. In particular you need more experience with variables, Items, and the difference between the two.