How to retrieve min/max values and corresponding dates in a table

Question

I'm trying to figure how to retrieve minimum/maximum values and minimum/maximum dates from a data set, but also the date value that corresponds to each minimum/maximum value.

Example Data:

CREATE TABLE mytable
    ([ID] int, [TEMP] FLOAT, [DATE] DATE)
;

INSERT INTO mytable
    ([ID], [TEMP], [DATE])
VALUES
    (8305,  16.38320208,  '03/22/2002'),
    (8305,  17.78320208,  '11/15/2010'),
    (8305,  16.06320208,  '03/11/2002'),
    (8305,  18.06320208,  '02/01/2007'),
    (2034,  5.2,  '03/12/1985'),
    (2034,  2.24,  '05/31/1991'),
    (2034,  6.91,  '09/15/1981'),
    (2034,  7.98,  '07/16/1980'),
    (2034,  10.03,  '03/21/1979'),
    (2034,  6.85,  '11/19/1982')
;

I'm struggling use Common Table Expressions to obtain both Min values & associated date, Max values and associated date, AND the actual min/max dates from the whole dataset in the same query

;WITH cte AS
(
   SELECT *,
         ROW_NUMBER() OVER (PARTITION BY ID ORDER BY [TEMP] DESC) AS rn
   FROM mytable
)
SELECT cte.ID, 
    COUNT(*) AS COUNT, 
    cte.TEMP AS MAXTEMP, 
    cte.DATE AS MAXTEMPDATE,
    MAX(mt.DATE) AS MAXDATE
FROM cte
    INNER JOIN mytable mt ON cte.ID = mt.ID
WHERE rn = 1
GROUP BY cte.ID, 
    cte.TEMP, 
    cte.DATE;

Edit 1: Expected output per user

|   ID | COUNT |     MAXTEMP | MAXTEMPDATE |       MAXDATE |       MINTEMP | MINTEMPDATE |    MINDATE|
|------|-------|-------------|-------------|---------------|---------------|-------------|-----------|
| 2034 |     6 |       10.03 |  1979-03-21 |    1991-05-31 |          2.24 |  1991-05-31 |1979-03-21 |
| 8305 |     4 | 18.06320208 |  2007-02-01 |    2010-11-15 |   16.06320208 |  2002-03-11 |2002-03-11 |