A one-word synonym for "someone who wears his heart on his sleeve"?

Solution 1:

Such a person (and their behaviour) is unrestrained.

From Collins Cobuild Advanced English Dictionary:

unrestrained adj

If you describe someone's behaviour as unrestrained, you mean that it is extreme or intense, for example because they are expressing their feelings strongly or loudly.

Via WFMT`S Audio Library, via Chicago Tribune.com:

'Drury obviously enjoys his job ... and he is unrestrained in his enthusiasm.'

And from France 24:

Speaking to AFP on condition of anonymity, a former associate called Matovic "a phenomenon". "He is an extremely proficient communicator. He is unrestrained and sincere – sometimes too sincere," they said.

'Abandoned' and 'uninhibited' are other possibilities.

uninhibited adj

1 Expressing one's feelings or thoughts unselfconsciously and without restraint.

‘a lively and uninhibited girl’

[Lexico]

'Abandoned' may convey too much wildness, impropriety.