There is a new Best Evidence in Brief with among others, this study (with bold by me):
Lisa Kim and colleagues recently conducted a meta-analysis to try to identify whether personality characteristics are associated with effective teaching.The study, which was published in Educational Psychology Review, looked at 25 studies (total number of participants = 6,294) that reported on relationships between five teacher personality traits (openness, conscientiousness, extraversion, agreeableness, and emotional stability) and two teacher job-related outcomes (teacher effectiveness and burnout).
Overall, the results showed that teacher personality may be associated with teacher effectiveness and job burnout. For teacher effectiveness, extraversion was found to have the largest effect size (+0.17), and agreeableness the lowest (+0.03). The characteristic most associated with less teacher burnout was emotional stability (effect size =+0.21), and openness had the smallest effect size (+0.04). However, as the effect sizes for burnout were very small, the authors suggest that the results should be approached with caution.
The researchers also looked at whether the source of the teacher personality report (i.e., self-report vs. other-report) and educational level had any moderating effects on the relationship between personality and job-related outcomes. The findings indicated that other-reports of teacher personality were more strongly associated with effectiveness and burnout than self-reports. There were no differences in the strength of the associations between the educational levels.