A warm bath — to an excess in the centre … (3,3)

I believe the answer is:

hot tub

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'a warm bath' is the definition.
'hot tub' can be an answer for 'bath' (type of bath). I'm not sure about the 'a warm' bit.

'an excess in the centre' is the wordplay.
'an excess' becomes 'OTT' (short for over the top).
'in' indicates putting letters inside.
'the centre' becomes 'hub' (hub is a kind of centre).
'ott' placed within 'hub' is 'HOT TUB'.

'to' is the link.

Can you help me to learn more?

(Other definitions for hot tub that I've seen before include "bathing facility" , "Bath large enough for several people" , "Very warm bath" , "Jacuzzi" , "Outdoor bath" .)

I've seen this clue in The Guardian.

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