Exceedingly hot in apartment and going up (3,4)
I believe the answer is:
not half
'exceedingly' is the definition.
(I've seen this before)
'hot in apartment and going up' is the wordplay.
I cannot really understand how this works, but
an anagram of 'hot' is 'oth' which is present in the answer.
'and' could be 'n' (common abbreviation for 'and') and 'n' is present in the answer.
The remaining letters 'alf' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for not half that I've seen before include "I warmly agree!" , "Oh, yes!" , "Extremely" , "Very much (but less than 50%)!" , "A full pint?" .)