What is the best approach for performance when querying across multiple DB's

Question

We have a setup where our customers each have their own databases. We also have some shared databases that are used to hold things like module access, reports, customer server locations, etc.

We have a few queries that look like this

USING CustomerDB

SELECT 
    fields
FROM
    CustomerTable C 
    INNER JOIN SharedDb.dbo.SharedtableA A ON A.Id = C.SharedAId
    INNER JOIN SharedDb.dbo.SharedtableB B ON B.Id = A.SharedBId

Does it make a difference to query plans etc if we were to change the query so that it executes in separate spaces?

E.g

USE CustomerDb

DECLARE @SharedTemp TABLE (
    Id int NOT NULL
)

INSERT INTO @SharedTemp
SELECT 
    Id
FROM
    SharedDb.dbo.SharedtableA A 
    INNER JOIN SharedDb.dbo.SharedtableB B ON B.Id = A.SharedBId

SELECT 
    fields
FROM
    CustomerTable C 
    INNER JOIN @SharedTemp A ON A.Id = C.SharedAId

Thank you in advance for your insights