Crossword Genius

Simple wrap as temperature previously went up (4)

Ross

I believe the answer is:

toga

I'm a little stuck... Click here to teach me more about this clue!

'simple wrap' is the definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Perhaps they are linked in a way I don't understand?

'temperature previously went up' is the wordplay.
'temperature' becomes 't' (abbreviation).
'previously' becomes 'ago' (I've seen this in another clue).
'went up' shows that the letters should be reversed in order (I've seen 'goes up' mean this).
'ago' back-to-front is 'oga'.
't'+'oga'='TOGA'

'as' is the link.

Can you help me to learn more?

(Other definitions for toga that I've seen before include "Roman raiment" , "Got a cloak for an old Roman" , "draped cloth" , "Graph's y value" , "garment of old" .)

I've seen this clue in The Guardian.
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