Creating Stored Procedure in local db that references tables in linked server
You can't parameterize entity names into a T-SQL statement. In order to do this you need to (a) create the #temp table first, and (b) use dynamic SQL. Here is one approach:

CREATE PROCEDURE [dbo].[mystoredprocedure]
AS
BEGIN
  SET NOCOUNT ON;

  DECLARE @exec nvarchar(256),
    @linkedserv nvarchar(150),
    @linkeddb   nvarchar(150),
    @sql        nvarchar(max);

  SELECT @linkedserv = N'HOSTNAME\SERVER',
         @linkeddb   = N'remotedb';

  SELECT @exec = QUOTENAME(@linkedserv) + N'.'
               + QUOTENAME(@linkeddb) + N'.sys.sp_executesql';

  CREATE TABLE #TempTable([Options] varchar(64));

  SELECT @sql = N'SELECT (CASE LTRIM(RTRIM(ot.[COLUMN1]))
        WHEN ''''     THEN ''''
        WHEN ''THIS'' THEN ''THAT''
        WHEN ''NOW''  THEN ''NEVER''
        ELSE ''OTHER'' END) AS [Options]
    FROM dbo.TableOnLinkedServer AS t
    FULL OUTER JOIN dbo.OtherTableOnLinkedServer AS ot
      ON t.COLUMN1 = ot.COLUMN0;';

  INSERT #TempTable([Options]) EXEC @exec @sql;   

  SELECT * FROM #TempTable;
END
GO


You could do it all inside dynamic SQL, so if knowing the columns up front is a challenge, there is a way. But it's messy, assuming you actually need a #temp table, because then everything you do with #TempTable has to be done inside the dynamic SQL.

CREATE PROCEDURE [dbo].[mystoredprocedure]
AS
BEGIN
  SET NOCOUNT ON;

  DECLARE @exec nvarchar(256),
    @linkedserv nvarchar(150),
    @linkeddb   nvarchar(150),
    @sql        nvarchar(max);

  SELECT @linkedserv = N'HOSTNAME\SERVER',
         @linkeddb   = N'remotedb';

  SELECT @exec = QUOTENAME(@linkedserv) + N'.'
               + QUOTENAME(@linkeddb) + N'.sys.sp_executesql';

  SELECT @sql = N'SELECT (CASE LTRIM(RTRIM(ot.[COLUMN1]))
        WHEN ''''     THEN ''''
        WHEN ''THIS'' THEN ''THAT''
        WHEN ''NOW''  THEN ''NEVER''
        ELSE ''OTHER'' END) AS [Options]
    INTO #TempTable
    FROM dbo.TableOnLinkedServer AS t
    FULL OUTER JOIN dbo.OtherTableOnLinkedServer AS ot
      ON t.COLUMN1 = ot.COLUMN0;

  SELECT * FROM #TempTable;';

  EXEC @exec @sql;   
END
GO


Please look at the obligatory Erland Sommarskog article on dynamic T-SQL to ensure you don't end up creating an embarrassing SQL Injection vulnerability.