It's been very busy with work and personal travel, and family events. Looking ahead at the schedule, I knew that this morning before my first calls of the day was the only time I'd have in the next week to fly my personally owned aircraft, so I headed to the airport for just a few times around the pattern, to see the sunrise from the sky, keep the engine lubricated and to get some "me time" in the airplane. Winds were south at 170, 7 knots. Two other aircraft were sharing the pattern when I poured the coals on. Downwind on the first time around, I could tell that the winds aloft were stronger than the winds on the ground, due to the significant crab to the west it took to hold left downwind leg. One of the other aircraft got confused about where the rest of us were at in the pattern, and started asking questions about where the other aircraft (and then, me) were currently located. This is right where I'd normally confirm gear speed, drop the gear, throttle back a bit, and begin configuring for landing. In responding to the call from the other aircraft, I let distraction set in, and didn't drop the gear. I noticed that my airspeed was higher than normal (clue #1, less drag), and incorrectly wondered if the tailwind was affecting the "feel" of the aircraft... of course, we all know it would affect my groundspeed but not my airspeed. I reduced power a bit more to lower the airspeed into the flaps range, and noticed that it was at a lower manifold pressure than usual (clue #2). "BEEP BEEP BEEP BEEP BEEP". The gear warning horn blared. (clue #3) Brain: "That's odd, why am I picking up the middle marker at KXYZ from over here?" Speed now where I wanted it, a touch of power added, blaring horn stopped. Flaps 10. Crosswind call, turn crosswind. Still a little fast. Pull the power a bit more, trim for 75. "BEEP BEEP BEEP BEEP BEEP". (clue #4) Panel scan. JPI 830 "CLD -52". Brain: "Wow, cool, I didn't know that the JPI would give me a tone alarm for shock cooling!" Added a touch of power to temper the shock cooling "threat" (which, retrospectively, really wasn't a concern now, was it, in the first time around the pattern) and the horn stopped, and the "CLD -52" red alert went away. Cool. All good now. (NOPE!!!) Turn final. Running GUMPS check as I pull power a bit more for glidepath control. "BEEP BEEP BEEP BEEP BEEP" (clue #5) G-- GEAR. HORN - OMG!!! I finally figured it out. Gear down, green, run GUMPS two more times (what else might I have forgotten?!) and landed full stop to sort it out and get my brain back in the game. Next two trips around the pattern were not an issue. Takeaways: I'm a careful, cautious pilot. I have a strict "GEAR DOWN to GO DOWN" rule, and habitually drop the gear as I enter the middle downwind leg on pattern entry / in the pattern. The radio call broke my cadence. GUMPs is usually ran there too, and on crosswind, and on final. The airspeed differences than usual and the distraction of the gear warning horn took me out of my routine. Next time, if ANYTHING seems out of the ordinary, exit the pattern, hold, figure it out there. Pay attention to clues, don't "rationalize" them away (marker beacon, JPI alert, etc.). It's a good thing I pressured my mechanic to get the gear warning horn fixed this past annual. It's a complicated cam/microswitch setup on the carb's throttle plate, and it didn't work correctly in the past. I would hope that GUMPs check on final would have caught it, but have to wonder if absent the three times the horn went off, would I have actually noticed? Checklists... important, but honestly, who has time to pull it out and read it in the pattern? Do you, every time? Maybe I'll change that routine, too... or is that what GUMPs is for? Would I have missed pulling the checklist for the same reason I missed the downwind GUMPs? Just sharing the story to spark discussion. We learn from each others' mistakes. Candid discussion is valuable. Yes, I'll file a NASA report, even though this happened at an uncontrolled field. There is a good lesson there about how distraction almost lead to disaster.