Found this thread when my energy consumption said SourceTree was using significant energy.
ps -A | grep SourceTree confirmed the issue in this thread:
78926 ?? 0:00.02 /Applications/Sourcetree.app/Contents/Resources/SourceTreeLogin Please type 'yes', 'no' or the fingerprint:
78927 ?? 0:00.02 /Applications/Sourcetree.app/Contents/Resources/SourceTreeLogin Please type 'yes', 'no' or the fingerprint:
78928 ?? 0:00.02 /Applications/Sourcetree.app/Contents/Resources/SourceTreeLogin Please type 'yes', 'no' or the fingerprint:
78929 ?? 0:00.01 /Applications/Sourcetree.app/Contents/Resources/SourceTreeLogin Please type 'yes', 'no' or the fingerprint:
78930 ?? 0:00.01 /Applications/Sourcetree.app/Contents/Resources/SourceTreeLogin Please type 'yes', 'no' or the fingerprint:
78931 ?? 0:00.01 /Applications/Sourcetree.app/Contents/Resources/SourceTreeLogin Please type 'yes', 'no' or the fingerprint:
each process would die and linger for a bit as (SourceTreeLogin) and then restart the cycle.
Indeed, new machine, missing key on BitBucket.
Upon adding it, I changed the account authentication from HTTPS to SSH, and did sudo pkill SourceTreeLogin and things got under control.
Fixed in Sourcetree 4.2.1