How to check which genes affect a continuous phenotype

I want to test which genes affect a change in a condition. The condition is measured on a continuous scale. The data comes from micro-arrays and there are two batch effects to be accounted for.

I thought of performing a multiple linear regression on each gene separately. The continuous treatment would be the response variable, and the explanatory would be the gene expression and the two batch effects. Then I could take the p-value of the gene expression term and adjust it for multiple comparisons.

Is it a reasonable procedure? Are there much better ones?