MacBooks are really hard to clean without removing the bottom cover. It is easy to do though, so I recommend you remove the bottom cover, and even remove the fan, and clean with compressed air. This will help with heat. As the other poster said, it is likely not your battery but your GPU and CPU generating the heat and most MacBooks I have opened have a nice layer of dust matted in the fan which will definitely contribute to heat.
And as far as cycle count, it really comes down to how it is performing. Apple says a battery should last at least 1000 cycles but if the battery is holding charge and shows as normal condition then it is nothing to worry about.