It's my understanding that renice doesn't limit CPU usage, but rather adjusts the process's priority in the scheduler relative to other processes. So I don't think it would stop a process from eating up all available idle cycles, draining the battery, and ramping up the fan.

Also, I don't think there's a trivial way to get the PID of the process handling a particular tab.

In Chrome, Task Manager shows PID along with CPU & memory usage.