To see her is a Picture — Bee

The hint is as June in line four, something related to June-beetle, -grass, -berry, -apple, etc. Bee, hinted by June-beetle, fits the poem for the description of its sting.

Likely Dickinson used this poem to mock a female friend by attached it in a letter. In this case, picture and tune mean something artificial; intemperance is "immoderate indulgence in intoxicating drink" (OED 3); and June beetle is a pest.

To see her is a Picture-1
To hear her is a Tune-
To know her an Intemperance
As innocent as June-
To know her not-Affliction-5
To own her for a Friend
A warmth as near as if the Sun
Were shining in your Hand.
(F.1597/J.1568)
[1] her:: a bee. Picture:: a view of bee and flower.
[2] Tune:: its humming sound.
[3] an Intemperance:: an addiction to study its life.
[4] June:: June beetle, a hint on an insect and the name bee within.
[5] Affliction:: the pain caused by its sting.
[6, 8] own her, hand:: to held the bee in one's hand.
[7, 8] warmth, shining:: reaction after being stung.

Acres of pasture on the Cotswolds have literally been rooted up by grubs, chiefly, I believe, by that of the June beetle, but that of the cockchafer or May beetle, has not been idle. ─ The Farmer's Magazine (1842)