This dawned on me after having to degrease something with rubbing alcohol, it’s much more effective when the object is already preheated!
So, following that logic, this proved to be quite efficient:
First Step, warm your mouth and inevitable your teeth, with hot water from your tap for a minute – hot enough that you don’t burn yourself.
Second step, now that your teeth are hotter than usual – rinse your mouth with alcohol-based mouthwash like Listerine, but any generic brand with alcohol in the top ingredients will do. Use as directed.
Third step, brush your teeth, preferrably with a ultrasonic tooth brush like the Philips Sonicare – you’ll notice stains coming off easier and your teeth whiter after these steps!
Step four don’t forget to floss!