Have you done the cache wipe yet?
Is your cell signal always fine, or was it only fine when you were looking at it? Go to the Settings>Battery menu and look at the battery graph--does it show you what the cell signal has been over the span of a battery charge?
If the cell signal is always fine, and if the cache wipe doesn't help, then I'd suspect some app that's malfunctioning. When the phone gets really hot, does the battery also drain quickly? If so, the next time this happens, go to the Battery menu and see if there is an app that is using an unusually high percentage of battery.