'99 Civic Rough Cold Starts / Occasional Overheating
I have a '99 Civic DX, 5-speed, and for the last couple months I've been having trouble with cold starts. The engine turns over fine and fires, but it starts really rough and sounds like it's running on 2 or 3 cylinders. Many times it dies and I have to start it again. Giving it gas helps a little, but the rough running becomes even more pronounced, like it's missing a cylinder or two. After running rough for about 5 or 10 seconds, it suddenly recovers and runs smoothly from then on. After it starts running, the engine idle does seem to me to be a bit low for a cold start, but it is summer and I can't really tell what it should be. Warm starts are fine. I've tried changing the plugs and wires, and cleaned the cap and rotor (since they are relatively new), with no change. This problem is an annoyance for now, but I fear that come winter, I will have even more trouble starting in the frigid mornings.
I also am having a possibly unrelated problem with the engine overheating on this car. This also happens only on cold starts, and only occasionally (maybe twice in a week). After a cold, difficult start, I'll be driving down the road for about 5 minutes, and the temperature gauge will start rising past normal. I turn on the heat inside the car, and only cold air blows out. I'll be driving at normal or highway speeds, with the engine running perfectly smoothly, mind you, and the temperature gauge will continue to slowly climb to almost the red, when suddenly it drops down to normal, and at the same time, I'll start to get heat through the vents, and everything is fine after that. After this happens, I need to add about a cup or two of coolant to top off the radiator. I'm not sure if this is related to the rough starting issue, but it may have started around the same time. Mind you, I am careful not to peg the temperature gauge at the red. I'm not sure how safe it is to run the engine with the temperature close to the red, but this has been happening for at least a couple months, once or twice a week, and each time, the temp dropped to normal before it got to the red. I've tried flushing the cooling system several times (flushed the block, heater core, and radiator separately) with no sign of obstruction or clogging. I also replaced the thermostat, and checked the compression of the cylinders (all 4 are around 140psi).
I would appreciate any ideas on what I should check next.