Extradition is probably not the correct way to view things. Russia and Thailand have friendly relations, so what would happen in reality is:
1. Russia would cancel the passport of one of its citizens
2. Russia's embassy in Thailand would inform the Thai Ministry of Foreign Affairs
3. The Thai Ministry of Foreign Affairs would inform Thai immigration that the Russian citizen's passport has been cancelled. At this stage it doesn't matter what visa or extension you have, your passport has been cancelled so you are in Thailand illegally.
4. The Thai police arrest you for being in Thailand without the correct documentation
5. You are deported back to Russia.
No need to appear in front of a judge for an extradition hearing.