Is your H3 using coolant at all? If it is, could be a heater core, but you'd likely smell coolant and see a fogged up windshield if it were. Swipe the windshield with your finger...if you see a definitel 'clean' area where you swiped, then it could be coolant deposits. Turn your defrost on (engine warm), and point towards the sunset. If you see a definite gray haze, that's coolant deposits. Your heater core is probably going bad, or nearby hose connection (at the firewall).
Could also be a failing head gasket or other coolant leaks. A HG might be something to check out after you've ruled out other coolant leak possibilities. A lot of times a "shooshing" heater core, the actual root cause is a slowly failing headgasket. Engine cools down and air gets sucked in. Then pressure can push air out too. Sometimes head gaskets can fail over the course of several months, or even a couple yrs before they let go catastrophically. Look under the hood. When the H3 is fully warmed up, and like after you've driven it a while, squeeze the upper radiator hose. If it feels like a freekin' balloon with 25psi...that's a definitel sign. Also, look under the oil fill cap for milky-looking deposits. Pull out the dipstick in the morning (when cold) and look for milky deposits on the tip (coolant in the oil). Also, if you've seen the last few symptoms, take the time remove the spark plugs. If one looks real new and clean (like it was 'steam cleaned'), that's the weak area. If two next to each other are 'clean' then the HG's is probably delaminating between the cylinder bores. If it's a HG, deal with it right away, bc driving around with a bad HG is going to kill your catalytic converter sure as can be, then you'll be spending another couple hundred bucks for a new header pipe/converter.
More commonly the sound could also be caused by a leaky radiator/hose/water pump, etc. Leaky radiators are fairly common at the plastic caps. Again, air gets sucked in under vacuum when the engine cools off from hot to cold. On real cold mornings, small leaks at the hose clamps aren't uncommon. They usually stop leaking when everything warms up. But I see you're in CA, so probably not your issue. But investigate the radiator upper/lower seal areas for calcium/mineral deposits which would point to a leak. A guy can actually remove the caps, clean the seal and re-install it. But nobody does that stuff, except in developing countries. But that's an option (there's Y/T videos). Best to buy a new radiator if you find that.
Start by checking under the water pump weep hole with a flashlight and an inspection mirror. It should be 100% dry. If it's wet at all, your water pump is leaking and the bearings will soon fail. Then check the hose clamps and radiator tank (the plastic parts) for fuzz and/or leaks.
If it's not coolant, let us know ...I'll have to think a bit deeper....
Good luck!
