How do stealth aircraft reduce the Heat Signature?
The short of it is that it's really hard to hide the heat signature of a device that is powered by burning large amounts of kerosene and shoving those gases out behind it. IR stealth is therefore a secondary concern (or lower) to designers of stealth fighters, primarily because the IR signature only matters at much closer ranges where stealth technology itself has reduced value (you can hide from radar, and camouflage to an extent, but you can't disappear entirely from visual range).

However, there are some things that can be done to make an aircraft less than blindingly obvious to IR sensors. Here are a few:


High bypass. Not all of the air that enters a turbofan engine's intake enters the actual combustion chamber. Bypass air helps to cool the hot combusted air before it exits, reducing the IR signature. 

The A-10, not a "stealth" aircraft in the slightest, nevertheless operates in situations where MANPADS (shoulder-fired SAMs) are a big threat, so to reduce its IR signature it uses some of the highest-bypass turbofans ever put on a military single-seater, at a 6:1 bypass ratio. These high bypass engines, however, reduce performance at high altitudes and high airspeeds; neither disadvantage is a problem for the low, slow A-10's mission profile, but for a more high-performance air superiority fighter this is a big deal. 

High-performance jet engines in fighters tend to be relatively low bypass compared to airliner engines for this reason. The F-15 and F-16 were powered by a P&amp;W turbofan with just 0.36:1 bypass ratio, however this only increases IR signature by requiring higher fuel flow rates for the same thrust at lower speeds (lower bypass also reduces the effect of afterburners because there is less unburned bypass air to feed the additional combustion). 

The F-22 mitigates the efficiency losses of a turbofan with a variable bypass intake system, allowing it to function as a turbofan with similar bypass to other fighters (about 0.3:1) at low speeds and altitudes, but converting to a near-turbojet configuration (almost zero bypass) at high altitudes and supersonic speeds, which is more fuel-efficient than an afterburner (and so allows the F-22 to supercruise).
Exhaust baffles. The thing designers typically want to avoid at all costs is exposing the actual point of ignition and primary combustion in a jet engine to the ground; this makes the hottest part of a plane's visible IR signature within the plane itself instead of the stream of hot air behind it, allowing easy targeting by IR SAMs. Imagine being an SA-13 "Gopher" mobile SAM launcher and having these twin fireballs from an F-15E for a target:



To hide this massive heat source, stealth aircraft are designed with exhaust vents that mask the exit point of the engine's exhaust from observation by the ground. There's really not a lot you can do design-wise to mask the IR signature from directly behind the aircraft; it's the pilot's job to ensure nobody ends up at that angle within missile range. 

Northrop is a fan of directing exhaust out over the top of their fuselage designs. Here's the B-2; you can see the heat plumes of the exhaust trail, but the source of actual combustion is well within the engine housing, and with the aircraft at any altitude the exhaust vent itself would be totally obscured:



Here are the exhaust channels of the YF-23, which incorporated lessons learned from the B-2; notice the similarities in the strategy for directing the exhaust out over the top of the aircraft's trailing edge:



The F-22 Raptor uses a similar theory of tucking the engines way back behind exhaust ducts, but these ducts can move to vector thrust or open to allow afterburners, so for greatest effect the ducts are placed to the rear instead of over the top of the fuselage as Northrop's designs tend to:


EMR-absorbing materials. A basic part of stealth design is the use of materials that absorb radar, and designing the aircraft's surfaces with angles that minimize the number of surfaces providing a direct return at any angle, while remaining aerodynamic. Other materials can absorb other frequencies in the EMR spectrum including IR; the Space Shuttle's lower and leading surfaces were covered in special ceramic tiles that could absorb enormous amounts of thermal energy while being cool to the touch. A similar material, not quite as effective but also less delicate, is used to protect the exhaust ducts of stealth fighters, and this has a secondary effect of lowering the radiant heat signature of the engines because the exhaust nozzles stay cooler. The radar absorbing material used elsewhere has some capacity for absorbing heat on leading edges, which helps avoid good lock-on by all-aspect IR missiles, but it's not the material's primary job.


In summary, designers do try to minimize IR signature, but tactically, if an enemy can launch an IR missile at you you have already failed at being stealthy. An infrared missile launch requires the launcher to tell the missile where to look, and that means they must at least be able to look at you themselves (using helmet-cued AA missiles), if not point the missile itself or the tracking radar at you. The idea of stealth is to minimize the amount of time the enemy knows that you exist by being invisible on radar, so they can't see you coming until they spot you visually, at which point they're either already dead or have mere seconds to react. Then for a ground run it's "one pass and haul ass" to avoid reprisals from anti-aircraft systems, while for an air-to-air engagement the first plane to launch a missile has an extreme advantage (and thus the advantage starts with the first plane to know where the other one is).