I am not familiar with Grohe showers. However, I looked at the diagram for your valve on their website. It appears that the thermoelement part 47-111 is just that...the temperature control. For the faucet to drip, water has to be getting TO the thermoelement when it should not be. It looks like the "drip" would be caused by the stop valves ( hot or cold) , items 9 on the diagram, part number 08-355 ( 2 pcs, hot side and cold side).
However, don't go out and buy more parts on my say-so. I am just looking at a diagram for a valve I don't have my hands on. Get someone to look at it in person. Or possibly call Grohe customer service. If they are good, they can help you troubleshoot.