I don't really like to get scientific as I'm not a scientist but, crunching some numbers and taking a few observations will save you a lot of time and some money with failed attempts.
You need to consider the pump, how quickly the water flows through the tubed coil, the length of the coil or tubing which gives you the time that the water has an opportunity to heat up. How far away is the point of use and any holding tank if any are considerations. The size of the tubing is also a factor.
The length of line in the coil around the heat source determines the time the water can heat at a given temp. The gap or distance of the plumbed coil from the exhaust pipe will also be a factor. You don't want it on the exhaust pipe as it shakes and moves which plays on the water connections and lines.
Counting on a few minutes of heat will not be sufficient while the exhaust pipe cools off at shut down. That is an observation based on successful systems. There is not much difference between heating water from exhaust attachments on a marine engine to one on a vehicle, engines and running temps are very similar if not the same.
If you run water through pumping at 6 gpm, through a 1/2" line that's 10 seconds a gallon.
Now, how cold is the water? What is the desired temp at the faucet? Just saying "knock the chill off" if that is the goal it will likely be met by the placebo effect, your expectation of the chill being knocked off through your contraption may lead you to a successful conclusion as you get wet while you bear a one degree difference.
Without going into rocket science and physics with heat transfer and velocity of water, let's look at how the problem has been solved by mankind to date. Look at the specifications of other engine driven water systems. Look at the replacement parts available for commercial heaters, a good unit should have a parts list. Most heaters are used in marine applications, used on yachts for decades. I suggest you study those units as they work well.
Turning tubing 6 wraps around the end of an exhaust pipe isn't going to get you squat nor will the temp be hot enough to significantly change the water temp being pumped through it at any useable pump rate. Maybe an aquarium pump would be slow enough rate allowing time to heat but doubt you can shower off at the rate of an I.V.
Copy what has already been done, you can make your own and many do on boats. You might be able to buy some parts. You'll need to heat during operation and have a holding tank, circulate the hot water keeping it hot, you'll need a thermostat at the tank unless you want it to explode, a pop off valve, and regulate the flow as needed. Otherwise, you'll need to run the engine while you tap off hot water as it's made.
