Right now I'm looking at both hot weather and temperate-to-cold weather boots.

I've actually begun with my search with separate terms.

For hot weather/muggy the only viable option I seem to find is the typical Jungle Boot.
Anything else out there?

For temperate-to-cold there are a multitude of options.

Hot weather seems to be the sticking point (badum-tish)

While I'm intentionally looking at high top boots it is more along the lines of providing ankle and lower leg protection vs support.  In fact I feel that puttees/gaiters with cross-country shoes may also fill the need.

Salomon for hot weather

I'm wearing Keens these days. Both for current warm weather, and I have a cold weather Keen waiting for snow to arrive.

Merrell Moab 2 Mid Vent were so comfortable I bought a companion pair of Moab 2 Mid Waterproof.

Oboz.

Oboz Sawtooth non-waterproof shoes for all but the most rugged warmer-weather hiking. Asolo Fugitive GTX and Lowa Camino GTX for really rugged terrain and cooler weather (down to around 20F or so.)

It seems to be all the rage to tell about how waterproof breathable membranes like Gore-Tex make your feet hotter in warm weather but that’s never been the case with me, and I’ve worn Danner Ft Lewis insulated boots in Korea and Saudi Arabia. My feet were nearly as dry as they would have been if I’d been wearing jungle boots. The Danners were more comfy, though.

How much weight do you plan on carrying?  You said "cross-country", so I'm assuming off trail?  Off trail with a heavy load is no joke.  While I'm a huge advocate for Salomon (and the like) cross-trainers for trail use, going off trail requires a different type of footwear.

Weight is always a concern for me, but it should be balanced with construction.  I simply don't care for Gore-Tex or any water-barrier liners anymore.  They may work well in sub-freezing/dry environments, but if it's going to be wet, hot, and your feet sweat, I would avoid them entirely.  With quality leather boots, you can keep them quite water resistant and you use wool socks to keep water away from your skin and/or thermoregulate your feet.

You'll likely get a ton of recommendations. Best advice for serious boots meant to go off-trail with a heavy pack, find a place to try as many on as you can.  These types of boots require a break-in and are stiff for a reason.  I don't hike in them much, but my Zamberlan 1023 Latemar NW boots are my broad-spectrum boots from warm weather to cold weather for all off trail activities/hunting.  They're an investment, and I've had them 6-8 years; used mostly for a couple of treks up mountains and late season hunting/scouting.  While these particular boots are listed as "warmer" weather boots, anything above 60 degrees and my feet heat up...

If you really need waterproof footwear, consider a pair of Gore-Tex socks.  Just know that if your boots get soaked from a slip in a river or trekking in a downpour, it will take days for your boots to fully dry out and they likely won't during an extended back-country trip.

For hot weather boots, I've quite happy using both Belleville's Minimalist combat boots and Salomon's Speed Assault boots (both being used in Afghanistan right now).  While I hike in low-top Salomon shoes and know their construction is solid, I can unabashedly recommend Belleville's minimalist boots if you consider that type of footwear.  They're not the best for carrying a heavy lead, but are quite robust, light footwear.  Lots of great choices these days, but getting them on your feet and getting the right sizing is quite important.

ROCK6

Pretty funny, I did the same thing.    I also have a pair of the low cut or hiking shoes (whatever they call them now) that I actually wear more than the boots; sometimes I use low cut gaiters with them as well.

Some years ago I started wearing lighter boots and haven't looked back; I even hike in Tevas or Chacos at times.  Unless you really need them for support or you're carrying a really heavy pack or you need to be able to strap crampons/skis/snowshoes/etc to your boots I just don't see the need anymore.  Boots are a very subjective subject though and what works for most people may not work for you.  I need a slightly wider shoes with a wider toe box after breaking a small toe and most European sizes are narrower in the toe in my experience.   I'm usually barefoot or wearing some sort of river sandals when I'm not wearing shoes for work so I'm used to the lesser support too.  Unfortunately finding bots that work for you usually requires some trial and error and once you do the manufacturer will feel the need to discontinue that model or change it.