The Chinese air force has at least two new stealth warplanes. And that’s a big problem for the U.S. Navy, which is still working on a radar-dodging fighter of its own.

The Navy’s quandary: how to shoot down Chinese planes that can’t be detected by radar — before the Chinese jets get close enough to launch missiles of their own.

One possible solution: to use the enemy jets’ own heat against them.

At the Paris air show on June 19, an official from U.S. munitions-maker Raytheon told reporter Bill Sweetman that the Navy had made an “urgent” request for a new, long-range, heat-seeking missile.

Raytheon vice president Harry Schulte told Sweetman that the new missile was specifically meant for dealing with “a particular threat that presents difficulties in RF,” or radio frequency (a.k.a., radar).

Sweetman asked if the threat was Chinese. “It could be,” Schulte replied.

His coyness belies the pace and potential sophistication of Chinese warplane development. The J-20, Beijing’s first radar-evading warplane type, debuted in December 2010 in blurry photos posted on the Chinese Internet. The smaller J-31 first appeared in September last year and other stealth models are rumored.

Both confirmed planes are still in testing, and little is known outside the Chinese government about their capabilities. But an analysis by Air Power Australia, an independent think tank, concluded that “no fundamental obstacles exist in the shaping design of the J-20 prototype which would preclude its development into a genuine very low observable design.”

The J-20 could enter service as early as 2018 — up to a year before the Navy’s own stealthy F-35C Joint Strike Fighter joins the fleet. Perhaps not coincidentally, the Navy wants its new infrared-guided missile to enter final testing in, you guessed it, 2018.

Paired with a new heat sensor being developed for the Navy’s current frontline jet, the F/A-18E/F Super Hornet, the new missile could exploit a possible major vulnerability of the Chinese stealth fighters: the heat generated by their radars, engines and other components.

Whereas the latest American warplanes including the F-35 and older F-22 use special fuel systems that absorb some excess heat, the Chinese planes are thought to be thermally unshielded. In principle, an infrared-homing missile could lock onto a Chinese stealth jet even if a radar-guided missile can’t.

But most current U.S.-made IR missiles have a fairly short range: just 22 miles for Raytheon’s latest AIM-9X Sidewinder. A J-20 fitted with PL-12 radar-guided missiles could fire on U.S. jets at nearly twice that distance.

Schulte said an urgent new IR missile for the Navy could overlap with the 40-mile range performance of America’s AIM-120 radar missile, at least matching the Chinese PL-12.

To develop this new missile fast, Schulte said Raytheon could increase the diameter of the existing Sidewinder missile body from the current five inches to six and fit a new, more powerful motor plus other improvements.

The resulting munition could at least give Navy jets a fighting chance against the latest Chinese planes.

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