I've never seen a properly running Honda product ever run hotter than approx just to the cool side of the mid-point on the temp gauge. Have had Legends, Tegs, and Accords, plus sold them for a couple of years (new & used), so I've had lots of exposure to new ones and old tired ones. . .

That 'little button' in the center of the radiator cap is to release pressure (hot steam and fluid) before removing it, so you don't get burned, or crap up the engine bay with coolant spraying all over. Some aftermarket caps have a little lever on top of the cap that does the same thing. I'd suggest switching back to an OEM cap, as they will have the correct pressure capacity for your specific car. And they are proven to work just fine on millions of other Honda products. Also, only use Honda brand coolant, no matter what an aftermarket brand claims, and do not alter the recommend mix ratios - too much coolant will defeat the intended purposes, both for low temp anti-freeze protection and for hi-temp protection. The alloys in most engines these days require a specific type of coolant, and that applies to Hondas especially, and using improperly formuated coolant will lead to undesired chemical reactions inside the cooling system (engine, heads, radiator, etc.) I've seen pictures of the internal passages that are corroded, plugged up, etc. from using offbrand coolant - worst thing you can do is use Toyota coolant in a Honda. . .While you're at it, install a new thermostat, as the one you have may be an improper heat range thermostat (they can be had in 180, 195, and even higher temp ranges - get an OEM replacement from Honda and do it right). And you'll need to properly bleed your cooling system after you change the coolant - follow the directions in the service manual for both draining and refilling the system - you need to get all the old fluids out, and get all you can back in without any air bubbles.

Also check your vacuum lines for possible leaky connections or cracks, and make sure your PCV valve is functioning okay. Either will cause all sorts of wierd idle issues, especially when accelerating from an idle position.

Also, don't overdue the fuel injector cleaner - I had problems w/ a Taurus SHO using an aggressive cleaner, and it actually screwed up some of the injectors, which were old orig. ones - may have dislodged some crap and affected the spray pattern. Besides, you'r wasting your $$, for name brand gasoline should have just about all you need in their gas already.

A fouled plug from a bad injector, or a bad plug wire (that can also lead to plug fouling) may be what's causing your idle problems. Improperly gapped plugs, or a cracked insulator should be the first (free) thing I'd check out. Also check for a crack in your distributor cap, or traces of moisture in there. Replacements are cheap at Honda. When reinstalling your plugs and wires - use a small amount of di-electric compound inside the spark plug boots at each end - I use MotorCraft from Ford because it's cheap and I have had a tube on hand for years.

btw: On a 2nd gen Teg we have, the coolant fan (for the radiator - not the AC) will sometimes run for several minutes after the engine is shut off - usually on a very hot day, or after running it hard. It has stuck on in the run mode more than once, and turning the engine back on, and then immediately turning it off, will cause the fan to quit running - never figured that one out).