Find the column names of Temp table

To get only columns name you can use this query below:

SELECT * 
FROM tempdb.sys.columns 
WHERE [object_id] = OBJECT_ID(N'tempdb..#temp');

To get columns name with data type you can use this query but you need to make sure sp_help runs in the same database where the table is located (tempdb).

EXEC tempdb.dbo.sp_help @objname = N'#temp';

you can achieve same result by joining against tempdb.sys.columns like below:

SELECT [column] = c.name, 
       [type] = t.name, c.max_length, c.precision, c.scale, c.is_nullable 
    FROM tempdb.sys.columns AS c
    INNER JOIN tempdb.sys.types AS t
    ON c.system_type_id = t.system_type_id
    AND t.system_type_id = t.user_type_id
    WHERE [object_id] = OBJECT_ID(N'tempdb.dbo.#temp');

SELECT *
FROM   tempdb.sys.columns
WHERE  object_id = Object_id('tempdb..#sometemptable');