S. R. Faruqi:

In this verse there are several kinds of excellence. The first is that in the first line the phrase ḳhvurshīd sāñ is in fact an interposition; its connection is with the second line. That is, the prose reading of the verse will be: agarchih mīr jahān se gayā valek majlis-e dunyā meñ ḳhvurshīd sāñ us kī jā garm hai .

The second point is that after the sun goes down, the redness of twilight remains in the sky for some time. Using for this redness the metaphor of heat, he's said that the way even after the sun goes down its place remains warm for quite a while, in the same way even after Mir's going his place in the world is warm. By the place being warm is meant not merely that his effects/traces remain, but rather also that no one can sit in his place. His sitting-place is warm, as if he has just now risen and left, and will very quickly come back.

The literal meaning of majlis is 'place of sitting'. In this regard, among majlis and jā and gayā there's the pleasure of a zila.

Then, jā garm dāshtan is a Persian idiom. In [the dictionary] bahār-e ʿajam its meaning has been given as 'to obtain stability and comfort'. This meaning is suitable for jā garm kardan , but this is not what jā garm dāshtan means. (In bahār-e ʿajam both expressions have been given as synonymous.) The truth is that jā garm dāshtan means 'by means of some place-holder, or in some other way, for one's place to remain secured, so that upon coming back one's place would again be able to be obtained'. Thus this [Persian] verse of Mulla Nisbati Thanesari, which is noted in bahār-e ʿajam , well illustrates this meaning:

'I leave my heart in her street when I go abroad
So that for some days it would keep my place warm.'

In the verse below, Mus'hafi has translated jā garm kardan as jā garm karnā , meaning 'for some while to settle and stay':

ham karne nah pāʾe the chaman meñ abhi jā garm
jo āʾī uṭhāne hameñ ho kar ke havā garm

[we hadn't yet managed to 'warm our place' in the garden
when the breeze came to make us rise, having turned 'hot']

In [the dictionaries] āṣifiyah , nūr ul-luġhāt , and Fallon's, neither of these idioms appears. In the dictionary of the Taraqqi-e Urdu Board, Karachi, jā garm karnā appears on the authority of Mus'hafi, but jā garm rakhnā does not appear even there; jagah garm karnā is there, but without a 'warrant' [sanad]. (The warrant, I will provide below.)

The meaning of jā garm karnā is almost the same as that of an English idiom. According to the Oxford English Dictionary, 'to keep someone's seat warm for him' was first used in 1845. From the date of its first use the thought occurs that it's possible that the English might have learned it from Hindustan, whether through Urdu or Persian.

In any case, in Mir's verse the loftiness [taʿallī], the metaphor, the idiom are all three very fine.

The theme of jā garm karnā , or jagah garm karnā , Jalal too has versified very well, although the meaning in his verse is virtually the same as in Mus'hafi's. Jalal's verse is:

biṭhā ke bazm meñ us ne vuh sard-mahrī kī
jagah bhī garm nah kī thī kih sard ho ke uṭhe

[having seated us in the gathering, she showed such a cold welcome
we hadn't warmed even our place, when we became cold and rose [to go]]

In both Mus'hafi's and Jalal's verses the wordplay is fine, but there's not that universality of meaning that's present in Mir's verse.

In our time, Iqbal Sajid has well versified Mir's theme. It's a pity that his first line is very flaccid, and its conspicuous word ramaq has been used in an incorrect sense:

ḳhvurshīd hūñ maiñ apnī ramaq chhoṛ jāʾūñgā
maiñ ḍūb bhī gayā to shafaq chhoṛ jāʾūñgā

[I am the sun; when I go, I will leave a spark of myself behind
even when I go down, then I will leave the sunset-glow behind]

[See also {456,8}.]

FWP:

SETS == GRANDIOSITY; MIDPOINTS; SUBJECT?
MOTIFS == GATHERINGS
NAMES
TERMS

SRF declares that ḳhvurshīd sāñ belongs only to the second line; to me, it seems a classic 'midpoints' case in which it could belong to either one; though even then, to my mind the first line is a better fit. There's no reason that Mir (1a), or the beloved or even God (1b), couldn't (metaphorically) leave the world just as the sun leaves the world-- depriving it temporarily of a warm, radiant presence, but with the assurance of a return in due course. In such a case it wouldn't be at all strange to find that the departed one's place was still 'warm' either because the departure was recent, or because the departed one's return was so eagerly desired or anticipated.