Does anyone make recordings in thermal cups, similar to STANLEY cups? What are the recording parameters like using EZCAD?

EZCAD is  laser marking software, i think you want mark something on the cups. the key parameters are the laser power and marking speed.  usually the laser source is fiber laser. and the working style is a rotary marking. 

Are you talking about using laser engraving patterns or text on metal insulated cups? This is very common, and the specific parameters vary depending on the actual item and material