Electrical Distribution

In the United States, most residential electrical service is what's known as a split-phase system. Which is a 3 wire, single phase system. The service entrance cable consists of two ungrounded (hot) conductors, and one grounded (neutral) conductor. Once at your house the grounded (neutral) conductor is bonded to earth, and a fourth conductor is added to the system. The fourth conductor is the equipment grounding; or simply grounding, conductor.

But why 4 wires?

A split phase system is aptly named, because the transformers secondary is center tapped (or split). This allows the system to provide different voltages, depending on how devices are connected.

120V

If a device only requires 120 volts it will be supplied using one grounded (neutral) conductor, either one of the ungrounded (hot) conductors, and one equipment grounding conductor.

240V

If a device requires 240 volts it will be supplied with two ungrounded (hot) conductors, and one equipment grounding conductor. In this case a grounded (neutral) conductor is not required, since the circuit is completed simply by connecting a load between the two ungrounded conductors.

120/240V

Some devices require both 120 volts, and 240 volts. These devices will be supplied with both ungrounded (hot) conductors, a grounded (neutral) conductor, and an equipment grounding conductor.

But wait... The old one only had 3 prongs?

In the olden days, we didn't care as much about safety (there were fewer lawyers around). Before houses were wired with the equipment grounding conductor, devices that required both 120 volts and 240 volts would be supplied with both ungrounded (hot) conductors and a grounded (neutral) conductor. Since there was no equipment grounding conductor, the circuit lacked one. This is why older homes only have 3 prong dryer (and stove) receptacles. The old three prong receptacles are NEMA 10 devices, and consist of two ungrounded (hot) conductors and one grounded (neutral) conductor (hot, hot, neutral).

Go the stove manufacturers' websites and read the installation manuals for the stoves, checking particularly for installation clearances.

You could also replace the drywall behind the stove with 5/8 or 1/2" (depending what the surrounding drywall is) tile-backer (cement-board) and/or cover it with 1/4, 1/2 or 5/8" spaced off the wall surface by 1/2" to 1" (look up "woodstove wall-protectors" for the idea) and cover with aluminum foil if going for the last bit of effect. Aluminum sheet (flashing material) spaced off the wall has a similar effect (radiant barrier.)

You may well have damaged (or missing) insulation in the back of your current stove if it's heating the wall that strongly.