1998 lexus es300

check the owners manual

There isn't a fuse. Clocks are very low voltage and ampere draw. Access the plug. Pull it and replace it(corrosion). If it starts working agian, you are good to go. Otherwise replace the clock module.

dose it work or warm up when you press and hold it down

Pop the Center Panel, Remove it from the Inside. There is a Single Wire that needs to be removed

On this website, you find fuse box diagram and description for Lexus ES300 (1998)

Lexus ES300 1998 fuse box diagram Auto Genius

Most likely a fuse, or a faulty lighter.

Stop smoking and it won't be a problem

I had the same problem on my '97. I ended up taking out the lighter when I was replacing the LCD on the radio, only to find that somehow it had become disconnected. Not sure how it happened but it might be worth checking out to see if it wiggled loose. To get to the lighter: 1) Prior up the cover by the shifter (the one that also goes back to the seat heater). It is connected with snaps so pry slowly. 2) Once the panel is removed you will see screws that are holding in the ash tray/cig lighter. Unscrew those and the whole lighter/ash tray can be pulled out. It is also held in by snaps on the top.