Here's what you do: State the obvious.
First, computer cases are only as cool as the air surrounding them. Due to the heat output of components (CPU, GPU, MOSFETs, soundcard, networking chips, northbridge RAM, PSU, hard drives, and anything else with power running through it!), even the coolest rig will be 5-10C warmer inside than the ambient temperature. IF IT IS EXPOSED TO SUN (ie: heat radiation) IT WILL BE WAY HOTTER THAN THAT!!! So clearly you'd need shade to even attempt it. Anyway, figure out what temp it is in the shade, then add the 5C (be modest). With 45C shade you're at 50C. Then the CPU is typically going to be another 10C warmer than that at idle, and 20C more at Load. That puts you at 60C idle, 70C load. Since most CPUs will either throttle or outright shut off before or around 70C to protect themselves from burning up, you can see that running a computer in an ambient temperature of 45C is asking for trouble.
That being said, P4s can handle temps up to 95C without dying (although both Northwoods and Prescotts will shut off around there), and Athlon 64s will shut down closer to 70C, so the P4 would be the choice if you were to make an attempt. Plus, I wouldn't do anything so mean to an Athlon. They don't deserve it, really. Prescotts though, those things are born in fire. Burn away!!
If you were to water cool it would be better, but assuming your reservior will heat up to ambient temperatures sooner or later, that will only buy you 10C leeway. Expensive alternative. CHILLED WATER might work, but if you've got water running below dewpoint in a hot environment you get what, childrens? That's right: Condensation. Frzzzzt!!! Baaaaad idea. A/C in a computer room isn't just good for cooling, it's also good for humidity. Humidity and heat will wreak havoc on any attempts to run a desktop computer. Maybe you could buy one of those air-conditioned cases... forget who does that.