The other day I decided to use the info from,
https://www.eevblog.com/forum/testgear/hp-agilent-34401a-hidden-menu/msg4631059/#msg4631059to upgrade my 34401A (10-5-2) with 10mA on AC, TEMP Menu, Min:Max - sdev and pp, scale/calc:scale, custom aperture NLPC and save and recall states.
Not sure how much I will use them at the moment but time will tell.
One thing I mentioned was DIAGnostic:TEMPerature?, I tried it and got "+4.73000000E+01". Would I be right in guessing that is from the 23C nominal so 27.73C