Royal Spanish Football Federation (RFEF) president Luis Rubiales hit out at LaLiga for scheduling matches in midday heat.
Levante's clash with Sevilla kicked off at 12:00 local time (10:00 GMT) on Sunday and the game was paused numerous times to allow players to rehydrate, while Rubiales alleged a number of fans suffered heatstroke.
Grounds like Ciutat de Valencia provide very little shelter or shade for supporters and the RFEF chief criticised the decision to play the match outside of cooler evening temperatures.
The game ended in a 6-2 victory for Sevilla, and Rubiales suggested the RFEF could take back control of LaLiga if the issue was not addressed.
"If LaLiga keep crazy schedules, we'll get the competition back for 2019-20," said Rubiales on Twitter.
"It's a disgrace for fans and footballers. At more than 30 degrees [Celsius] you cannot play at certain times. Heatstroke for dozens.
"Inadmissible. In the RFEF we're fed up."
LaLiga president Javier Tebas quickly hit back with a response to Rubiales via social media.
"Dear Luis Rubiales," Tebas wrote on Twitter. "Today at the Aragon GP [MotoGP], 32 degrees and 114,000 people in the sun enjoying the races without complaints.
"By the way, at the RFEF's Evergrande Cup [youth tournament] in Las Rozas in August [it was] 36 degrees. You cannot recover what is not yours."
