bot_thinktime is the time the bot thinks in milliseconds (per q3 source).
I don't know if that means the bot plays stronger since he thinks longer, or he plays weaker since he does the same amount of thinking in a longer period of time and therefore makes a decision quicker when set lower, or carries out an action more quickly.
I would like to know for sure. If you can demonstrate a difference with a demo or whatever, I'd love to see it.
bot_thinktime is indeed the time a bot takes to think. So if you set it to 0 the bot has 0 msec reaction time and is therefore challenging. It will dodge quicker and shoot better rockets. I'll see if i can show it with a demo