Quick soapbox post. Some long time posters have heard it before.
I want to try to make a point to discourage the purchase of 4 channel amplifiers solely for the puropse of bridging the 4-channel amplifer to run a stereo load.
For many situations, there is a proper stereo amplifer that will deliver the same amount of power while operating at a comfortable 4-ohm load per channel, with the cool, (or cooler) operating temperatures and lower current draw that result from the use of a stereo amplifer.
For the OP's question regarding the ZX350.4, I would turn around and recommend a ZX450.2 or ZXM450.2.
The reasons are two-fold. First off, MOST 4-ohm speakers are nominally 4-ohms, but in fact, their impedance can be quite a bit lower for certain frequencies. 3.4 - 3.6 ohms is often the norm. This will cause a bridged amp to see less
than 4-ohms per side for some frequencies. This in turn shows each amp channel less
than 2-ohms; the minimum safe load it was designed to operate into.
Secondly Bridging an amp, or running a stereo amp at a nominal 2-ohm load take the amp to its max-current max heat operating condition. If I can draw an analogy, it is kind of like running a car or boat motor right at redline all the time. It is hot, it stresses things, and leads to things breaking soon. Sure you can bridge an amp, but why? Why take it right to the edge of its capabilities?
These two things, (lower than 4-ohm speaker impedance and trying to not run an amp right to its ragged edge) are the reasoning for my recommendation MOST OF THE TIME to use a proper higher-powered amplifier that will deliver the spekaers desired rated power at 4-ohms.
There are exceptions, so to play both sides, let me quickly explain.
The Kicker KM6500.2 and KM6500 tower speakers were designed from the beginning to address the first point aove. Specifically, the KM6500.2 is a true 4-ohm system that does NOT dip below 4-ohms. As such, it can be used on a bridged amp, knowing FOR SURE that the amp always sees 4-ohms and only 4-ohms, regardless of frequency. Each amp channel only sees 2-ohms and never less. ... As a result I will recommend the bridging of a 4-channel amp where higher power is needed. Such and example would allow the ZX350.4 to bve used without fear, as the OP asked, or one could go with teh IX500.4, which I currently recommend as the hot ticket for that speaker setup.
Back to the topic. For most "nominally" 4-ohm speakers, if you KNOW you are going to be running a pair of stereo speakers, and you need to buy an amp, try to buy a STEREO amp to run them. Use an amp that will deliver rated power to the speakers, while showing the amp a 4-ohm load. The sound will usually be better, the heat will be lower, the current will be less. and the amp will run longer before thermalling.
Finally, to clarify or add to what Shawndoggy is saying. Many Class A/B amps run hot. It is their nature. The amp in question as well asa other Kicker amps run hot too, but they have a thermal protection system in them to prevent overheating. If it is hot, but it is running , it is fine. When it starts shutting off is when you know you are too hot, not by being hot itself... You can maximize your cooling for the amp by doing a few things:
Always mount it on standoffs so that it is not against carpet. This gets air all arond it and helps shed the heat.
Use the recommended wire gage. HIgh current running, (most ot our tower speakers) will create voltage sag, which inturn will increase current flow in the amp. Low voltage actually makes the amp run hotter.
Get some air moving. Convection works wonders if you can have some way to allow the air in your amp compartment to change out. Fans will help, but many times, takign the opther steps first will eliminate the need for fans. they are cool to see in an install though, so cinsider it anyway.
Hope my soapbox discussio is helpful...