What can I do about my car's transmission?

Yesterday coming to work, my car started acting up. It is a 2003 Honda Civic Hybrid and what happened was 1) The "drive" indicator on my dashboard was blinking, 2) the engine light was on, 3) The car began shaking and sounded like something was rattling under the hood, 4) When stopped, the car would not accelerate. I had to turn off the car, turn it back on, and made it a few more blocks to my work.

Apparently, this damaged the car a lot more than if I had just pulled it over at the first sign of trouble. I had it towed to a mechanic, and here's what they said:

1) The cooling sensors malfunctioned due to overheating

2) The heat (over 400 degrees) also caused some damage internally to my transmission.

As a result, they said that the likely scenario is for the transmission to be replaced. However, I'm kind of skeptical. I don't know much about the cars, but this seems like more of a radiator/engine problem than anything.

Any help is appreciated, thanks.