I have a 2004 330i and for the past few days the thermostat creeps up to almost "red". It only happens when in idle or stuck in traffic. Also, a/c and heater both are not working.

Sounds like one of your cooling fans may not be working properly. Check to see if they kick on when your car is parked but running. You may have a seized fan motor or a bad temp sensor for the fan. Replacing your thermostat would be a good idea too. As for the grey smoke, your car may be burning a little bit of oil on start up due to worn valve seals. Does your vehicle have high mileage? If so, it's not uncommon to have some oil burning going on if you have over or around 150k on it.

My car has 124,000 miles on it. I have been disappointed in issues I've had - my Infiniti never had issues. Is this something I can do prior to taking to mechanic? Mind you, I am female and do not know much (anything) about mechanics but willing to learn to save $$$. Thank you for your help!

Btw, my service engine soon light has been on for awhile and this other light immediately to the right of that. It goes off and on at random. This has been an ongoing problem - the mechanic "flushed" something out and thinks it is a glitch.

That's the problem with European vehicles. If you want them fixed right you have to take them to the dealer or a shop that specializes in them. I am not a BMW guy so I really can't be much help as far as what the light means. If you are not taking it to a dealer, I would this time around. Sounds like you have some error codes that need to be taken care of. They should be stored in the cars computer. After they have been addressed, the dealer will clear them so your check engine light will not come on. Your car may be due for an oil change. Some vehicles service soon light will illuminate when an oil change is due. Check your owners manual and see if your car has that feature. Should be in your glove box. I take it you haven't been taking it to a dealer since the mechanic gave such a general description of your issue. Clearly the problem wasn't fixed the first time around. I would stop throwing money at it and get it fixed right this time. Then if you are that unhappy with it's performance, it would be a great time to trade it for a more dependable car. The downside to owning a BMW is that everyone thinks that if you have the money to own one, you have the money to fix one........

Heating up and heater not working are classic signs of trouble with the cooling system. Cooling fans and thermostat trouble, as Reelin68 says, are two strong possibilities. However, an equally likely one is that you're low on coolant. Did you have an incident in which steam rose from the engine, or do you see any signs of steam leakage when the engine is hot and you're not moving? Could be a bad hose or other leak or a clog due to corrosion (using water instead of coolant can cause corrosion). This is something almost ANY independent, non-BMW repair shop ought to be able to diagnose cheaper than BMW (unless you have some sort of warranty, which seems doubtful given your mileage). As for an intermittent "service engine soon" light: this is a royal pain-in-the-butt problem to diagnose. It can be caused by a non-sealing gas cap, big change in altitude, DMTL pump going, or other emissions-related items slowly going bad. Probably not oil; that would appear on your dash with its own warning. You need to go to a shop with the BMW code reader (BMW has its own codes in addition to the standard ones). That's either a dealer or BMW specialist.

Regarding saving money generally on a BMW: Search for your problems on Bimmerpost and other user-comment sites. Sign up with Bimmerpost and ask questions. One thing which is absolutely certain: the dealer will be the most expensive of the honest answers. Seek out a BMW specialist nearby. Read the Carguru, Yelp and other reviews. And if you can, learn to triage repairs. That is, some repairs don't need a high-priced specialist. (Coolant leak, for example.) The same is true of an oil change, spark plugs, brakes, and other basic maintenance items. If you know of an honest non-expert local shop that will say " We can't fix that one, take it to the dealer," start there.