businesslike

A long engagement , then marriage-Oh Bathsheba! promise yourself to me!
he begged wildly , forgetting his cool , businesslike manner.
Far from the madding crowd By Thomas Hardy.

In the wordreference dictionary , the meaning of ''businesslike'' is ;

busi•ness•like /ˈbɪznɪsˌlaɪk/ adj.

1. showing qualities that are good in business.
2. efficient but not warm or personal:

But in the sentence above it seems to have an other meaning , what is the meaning of ''businesslike'' in the sentence above?

Meaning 2: efficient but not warm or personal appears to fit Hardy's use of 'businesslike'
Especially as he emphasises the fact that his character is usually 'cool' (i.e. not warm or personal)

The fact that the character is wildly begging clearly suggests he has 'lost his cool'

It means number 2. Businesslike is the opposite of emotional.