I built a tig cooler using a diaphragm pump, the type typically use for agricultural sprayers. The pump is rated at 1.8 gpm @ 60 psi. It is made by Shurflo, and is periodically on sale at Northern Tools for less than $60. A
12VDC power supply is required; an old PC power supply works great. Even though the pump is rated for continuous duty the motor will become very hot after about an hour of use. I installed a small fan, also salvaged from an old pc, blowing on the motor. With a fan the motor runs cool even after several hours of continous use.
One characteristic of a diaphragm pump is that the pressure is pulsating. It does not deliver a constant pressure like a gear pump does. This is not a problem, because the hose leading to the torch is long, small diameter, and flexible. The hose works to average the pulses. I can feel a significant pulsation in the hose immediately after the pump, but there is almost no pulsation noticable at the torch, even with a 12' hose.
My system uses a 5-gallon bucket as a reservoir. A bypass valve is used to regulate the pressure. I have found that under most circumstances only around 40 psi is needed to cool the torch. I bump the pressure up to 50 psi when I am welding aluminum at high amperage. Due to the pulsations from the diaphragm pump, if you connect a pressure gauge you will need a "snubber" ahead of the gauge. I use a small needle valve for that. If you search the web you will find plenty of info to describe a snubber.
Overall, I spent about $90 on my cooler, most of that for the pump. Except for the pump and the left-hand hose fittings, everything was either salvaged or purchased at a local hardware store. It's ugly as a cow's butt, however it works well. I have noticed that during extended welding sessions at high amperage the water does become warm, but even so it still effectively cools the torch. You would need to be using big amps on a big torch to overwhelm the 4 gallons or so of water in the bucket. A radiator is probably overkill unless you are doing commercial welding at > 200 amps, or you live in a hot climate. Ten feet of 1/4" copper tubing in a coil on the return side of the circuit would probably be an adequate radiator for most home uses.
I also installed a safety fuse on the coolant return/power cable. This is a device that is inserted inline on the return hose. If water is not flowing or if inadequate water is flowing the fuse will blow and cut the power before the torch is damaged. I think I paid about $35 for that item. Be sure to buy some extra fuse links, they will occasionally fail because of arcing. It doesn't happen often but when it does you will need a spare link. The fuse links are cheap, about $7 or so for five of them - probably a 3-5 year supply.