hardly any assist from elec. motor

OK, with the "hybrid system coolant pump" replacement campaign going now, I read in the press release that failure of this pump may result in almost no use of the electric motors in normal driving.
Perhaps your pump has failed (if there really is a problem). I'm told you can see the coolant circulating in the fill chamber. I'd check this out. It may be your problem, and if your car is on the replacement list it's a warranty job. You can check here (there is a topic on it with a VIN list) or you can check at Toyota.com.

 

It depends how badly it (the inverter) is overheating. Before jumping to conclusions you should just check that your inverter coolant pump is running. With the car in ready mode, pop the hood and remove the cap from the inverter coolant reservoir. Looking straight down through the filler hole to the surface of the coolant, if it's running you'll see a little stream of turbulence. It's pretty easy to spot.

 

The battery equalization is something that the Prius does every few thousand miles or so. It's when it's system charges the battery to full (80%) and then uses EV mode aggressively. This has happened to me once where the electric motor was barley assisting and it kept charging the battery till it was full. It was weird and unexpected.