Credit to niuguitarman for the chords to the original, I've merely transposed it 
and added in the extra bits/key changes from Cocker's version. You could play it 
as Am with a capo on the 5th fret if you so wished, transpose it 5 steps down 
using controls if applicable.

[Intro]
Dm | Bb (repeat)

[verse 1:]
Dm (xx0231@1)        Dm/C (030231@1)              G/B (143121@7)                  Bb (x1333x@1)       A (x02220@1) Hot town, summer in the city; back of my neck getting dirty and gritty
Dm (xx0231@1)         Dm/C (030231@1)           G/B (143121@7)               Bb (x1333x@1)           A (x02220@1) Been down, isn't it a pity; doesn't seem to be a shadow in the city
A (x02220@1)            A7 (x02020@1) All around, people looking half dead
Dm (xx0231@1)                     DWalking (xx0232@1)on the sidewalk, hotter than a match head

[chorus:]
G (320003@1)                   C (x32010@1) But at night it's a different world
G (320003@1)          C (x32010@1) Go out and find a girl
G (320003@1)                    C (x32010@1) Come-on come-on and dance all night
G (320003@1)                      C (x32010@1) Despite the heat it'll be alright
    Em (022000@1)            AAnd (x02220@1)babe, don't you know it's a pity
         Em (022000@1)       AThat (x02220@1)the days can't be like the nights
       Em (022000@1)           AIn (x02220@1)the summer, in the city
       Em (022000@1)           AIn (x02220@1)the summer, in the city

[Link]
Dm | Bb (repeat)

[verse 2:]
Cool town, evening in the city; Dressing so fine and looking so pretty
Cool cat, looking for a kitty; Gonna look in every corner of the city
Till I'm wheezing like a bus stop
Running up the stairs, gonna meet you on the rooftop

[chorus]

[Link]

[Instrumental break]
Chords as verse

[chorus]

[Link to outro]
F#m | B (repeat)

[Outro] (Verse but up a tone)
Em | Em/C | A/C# | C B |