Firstly I have to suggest that is a very poor kick boxer. Secondly Thai Boxing is more designed for close in combat. An exponent of Taekwondo uses kicks greatly and obviously needs a certain distance between him and the opponent to carry this out. Thus putting him out of reach of the kick boxers own attacks.
The only way a kick boxer can win in such a contest is to cover up and use lots of upper body movement in order to try and deflect a lot of the kicks. With that he also needs to have the cojones to continue forward to eventually crowd the karate guy out and so defusing his threat.
How do I know this? I have been in a similar contest but this was against a 2nd dan black belt at karate who used a very european/boxing type approach. I struggled big time against him to land anything for points.