No, the battery is the smallest problem for heat. (Well, fast loading can cause a lot of heat)

For fun you may want to look up the TDP (Thermal Design Power) of your CPU and (if there is one) GPU of your computer. The TDP states what class of "venting" the Laptop needs to have for those parts. (It is not what the parts use, but this is a really complicated story.)

Now add those 2 up and look at the power block of your Laptop. Typical is ("writing" Laptop) e.g 60W. Now take 10W for the screen, the TDP of CPU and GPU and look what is left. That is - very roughly - the amount of heat that all the other components can use.