Tex. Code Crim. Proc. art. 43.16
Immediately upon the receipt of such warrant, the sheriff shall transport such condemned person to the Director of the Department of Corrections, if he has not already been so delivered, and shall deliver him and the warrant aforesaid into the hands of the Director of the Department of Corrections and shall take from the Director of the Department of Corrections his receipt for such person and such warrant, which receipt the sheriff shall return to the office of the clerk of the court where the judgment of death was rendered. For his services, the sheriff shall be entitled to the same compensation as is now allowed by law to sheriffs for removing or conveying prisoners under the provisions of Section 4 of Article 1029 or 1030 of the Code of Criminal Procedure of 1925, as amended.
Tex. Code Crim. Proc. § 43.16