Do It Yourself

Well there is plenty of reason to not do it, but I'm assuming you've thought about what tampering with your water supply means (and that car radiators are not food safe, and could contain lead or other nasty metals). I think it goes without saying you're also running the risk of leaks, a high water bill, and mornings without water if your system has issues.

I'd also like to cover my ass a little and do the typical engineer thing and remind you that an idealized number like this is never realized. You will have to account for losses due to inadvertent and incomplete heat transfer. But you may also get a higher reduction due to the ground heat exhange, which I am still too lazy to work out. ¯⁠\⁠_⁠(⁠ツ⁠)⁠_⁠/⁠¯

All of that said, I really hope you succeed at getting cheaper cooling and have fun doing it. There are houses which use water piped through concrete flooring to regulate temperature, so you're not very far in uncharted territory. Doing big projects like this are also a really good way to learn a lot very quickly.

I also still highly recommend getting a quote for a reputable geothermal cooling system. If nothing else but to brag about how much you saved by DIYing

Engineers describe heat transfer with a "heat transfer coefficient", and the rate of heat transfer is this coefficient multiplied by the temperature difference. So you can calculate what the heat transfer coefficient must be by measuring room air temperature initially, water temperature initially, and then running your system for a little while and measuring the room temperature again. The smaller room area you can cool the more accurate this will be. You will need to look up heat capacity and density of air (easy to find), and the temperature change of the air with the volume of the room and the temperature change will together give you an amount of heat you removed from the air to the water. Simple!