Not only is rice not particularly effective, it is very dusty (organic dust is the worse) and that dust will settle inside your watch if you have the back off.
If you don't like the desk lamp idea, possibly you have some Silica Gel Desiccant packs lying around? Use those in the zip lock bag with your watch, not rice.
If your silica gel packs are even a few days old, they've probably already absorbed their share of ambient moisture out of the air.
You can refresh them by putting them in the toaster oven and setting the temp very low and running it for 5 minutes or less. No, don't "toast" them or they'll burst into flame ;-)
Its not a bad idea to have some packs on hand. Store them in a zip lock.
https://www.amazon.com/Silica-Gel-Desiccants-2-1-Inches/dp/B003DKQB02