You can try Treebo hotels. It is budget friendly, and comfortable. Just make sure that you ask the staff to spray mosquito repellent in your room before you sleep. I had a very bad experience with the mosquitos.
And Kovalam is around 45 minutes drive from the temple. So, you can simply hire a taxi. Please keep in mind that the uber/ola drivers come to pick you up on a condition that you pay them Rs.100-200 above the fare that is showing in the application. So, be ready for that.