Prewarming for tankless waterheater
The typical way to pre-warm water is to install a standard tank water heater before the tankless, but leave it turned off.

Using an automotive radiator is a terrible idea. You don't want to connect something not designed for potable water to your plumbing. That's just asking for trouble.

The pex idea is interesting. The only reason that I can think that this wouldn't work is that 100 feet of pex introduces quite a pressure loss. Put a meter on the end to make sure you have enough pressure going in to your water heater. If you have the stuff to do that, you can try it out. But I wouldn't buy 100 feet of pex just to do it.

Using a tank water heater has a couple of advantages over the pex-in-a-bucket-of-water idea:


If your tankless water heater has a problem, you can just turn on the tank water heater.
You get pre-warmed water for much longer with a tank than your 100 feet of pex.

With the pex solution, most of the heat transfer is going to occur when the water is sitting in the 100 foot coil. When the water is flowing, heat transfer from the bucket water to the water in the coil is going to be minimal. So once you empty the coil, your pre-warmed water is gone.
With the tank water heater, the room temperature water in the tank will mix with the incoming cold water. You get a very slow gradual drop in temperature, but it doesn't drop suddenly after a few minutes like the pex solution would.

If you ever have your water shut off, you've got a whole tank of water available for you to use.