Challenge to fit a lm to every "gene" in df

df_fit_lm.R

df <- data.frame(gene = rep(c(paste("gene", 1:10, sep="")), 5),
                  treatment = rep(paste("trt", 1:5, sep=""), each=10), 
                  temp = rep(1:5, each=10),
                  exp = rnorm(50))
                  
head(df)

# lm for a single gene
lmout <- lm(exp ~ temp, data = df[df$gene == "gene1", ])

summary(lmout)
# note "p-value"