Shortly before the primaries in March, voters in Amarillo, Midland and Odessa received a two-and-a-half page letter in the mail from Tim Dunn, a wealthy local oil and gas developer.

“Dear fellow West Texan” Mr. Dunn’s letter began, before urging them not to vote for State Senator Kel Seliger, an Amarillo Republican who Mr. Dunn believed was not conservative enough.

“In every possible way, West Texas defines who I am as a conservative,” wrote Mr. Dunn, who generally tries to avoid publicity. “And I am saddened to see West Texas values not represented in Austin.”

The letter was not from Empower Texans or any of the other scrappy yet influential political groups that Mr. Dunn has helped finance over the last decade. It was an unusually direct appeal from Mr. Dunn himself, who, while not the biggest spender in Texas politics, has been widely seen as the most effective. Through a growing network of political groups that are often billed as grass-roots, and frequently aligned with the Tea Party, Mr. Dunn has invested millions of dollars into moving the Texas Legislature further to the right.