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.