Single-stranded RNA molecules can form intramolecular bonds between nucleotides to create secondary structures. These structures can have phenotypic effects, meaning mutations that alter secondary structure may be subject to natural selection. Here we examined the population genetics of these mutations within Arabidopsis thaliana genes. We began by identifying derived SNPs with the potential to alter secondary structures within coding regions, using a combination of computational prediction and empirical data analysis. We identified 8,469 such polymorphisms, representing a small portion (~0.024%) of sites within transcribed genes. We examined nucleotide diversity and allele frequencies of these "pair-changing mutations" (pcM) in 1,001 A. thaliana genomes. The pcM SNPs at synonymous sites had an 13.4% reduction in nucleotide diversity relative to non-pcM SNPs at synonymous sites and were found at lower allele frequencies. We used demographic modeling to estimate selection coefficients, finding selection against pcMs in 5' and 3' untranslated regions. Previous work has shown that some pcMs affect gene expression in a temperature-dependent matter. We explored associations on a genome-wide scale, finding pcMs exist at higher population frequencies in colder environments, as do non-PCM alleles. Derived pcM mutations have a small but significant relationship to transcript abundance, however; alleles containing pcMs had an average reduction in expression of 137.4 normalized counts compared to genes with conserved ancestral secondary structure (mean expression = 3215.7 normalized counts). Overall, we document selection against derived pcMs in UTRs but with limited evidence for selection against derived pcMs at synonymous sites.