Correlation between fixed effect and random effect in mixed model

I'm interested to study weather conditions on species diversity. To this end, I used a mixed model, where Julian-day, temperature, and precipitations are the fixed effects, while the month is used as a random effect. My question is: Is it a problem to use a random effect that is correlated with one of the variables in fixed term?

Random effects terms are used to account for correlations in grouped/clustered data. When you include a random effect for the grouping factor month, then you postulate that species diversity measurements in the same month are correlated. The fixed effects are used to specify the mean of your outcome variable (i.e., species diversity).