For thai boxing, it's all about the heavy bag - jumprope, and road work. And cross training with weights will improve the basics mentioned. Thus, if you're serious about this, get a heavy bag. However, because I've never tried hitting a tire before, where now you have the opportunity to try, and if you're really curious, why not give it a go. That is provided you still train with a heavy bag at your gym.
Another option is to make that tire into a bulgarian bag. Where you can do military presses with such, bench press the bugger, squat with it, farmer's walk, power clean, running from one place to another with that bugger on your shoulders. It's an awkward object, which will allow you a different kind of strength gain, which in turn will have carry over in your sport. :3
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Found this, you might like.