Green’s Dictionary of Slang

1. of language, obscene.

1885		Bulletin (Sydney) 7 Feb. 6/2: Oh, h--, but there! We will not use / A phrase that might be ‘tropical;’ / That theatre-board’s the very ‘push’ / To turn out philanthropical!
1902		Bulletin (Sydney) 18 Oct. 12/2: It was a hurricane of emotion. [...] There was a hot passion in his face. He was at a dizzy pitch of excitement. [...] Melba was palpably nervous, not quite sure whether to smile or give serious attention. She was faced by an educated Dan O’Connor. Occasionally, a demure shake of the head negatived a too-tropical compliment.

2. of stolen goods, illegal, dishonest.

1967		‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xli 4/4: tropical: Any goods not paid for by the possessor can be classified as tropical. How tropical, depends on what sort of fuss goes on to generate heat.
1983		R. Aven-Bray Ridgey-Didge Oz Jack Lang 47: Tropical Something stolen (hot).

3. intense.

1991

M.B. ‘Chopper’ Read Chopper From The Inside 66: It was getting a bit tropical and I had to ease it up for a while.

4. highly suspicious; very dangerous for criminal activity.

1993

Smith & Noble Neddy (1998) 278: All he was concerned about was whether I’d been followed. ‘Neddy, you are very tropical [hot] at the moment. I can’t be seen talking to you.’.