I just had new tires put on my 2016 BMW x3 about 3 weeks ago. There is a soft on and off rattling coming from the front of the car. Recently I've noticed when I stop at a light there is a burning smell. Similar to the new car smell when you drive it the first few miles. Today I came home from work parked in the garage and went back to the garage about 5 min later, and noticed a bad burning smell. Not sure if this is all related to the new tires?! Any insight? I am planning on taking it back to the shop.
The first thing I would do is check to make sure your handbrake (i.e. emergency brake) is completely off, if it's partially applied the brake shoes will constantly rub against the drums and the overheating will cause a smell as you describe.
Otherwise a strong burning smell could be many things, for instance an oil leak or insulation burning, however my money would be on a stuck brake caliper or something rubbing on a tire. You may be able to determine the cause with your nose, smell each individual wheel and see if the smell is stronger with one wheel.
If the smell is strong with both rear wheels that would indicate the problem is with the handbrake, if it's a single wheel it's most likely the caliper in that wheel. If it's a caliper then it could be caused by something done during the tire change, especially if it was straight after the change, although it could still be a coincidence. If it's something rubbing on a wheel then it's definitely something they did. If it is something else entirely it's unlikely their fault.
In any case you should get it looked at, there's no benign reason for a burning smell.
How many miles are currently on the vehicle? Based on the 7 year age, 120k miles would be average depending on your region. Do you have any aftermarket add-ons to the engine, exhaust, intake, or other items that may ring a bell? Check engine/MIL, DTC indications? I would suggest to look around the brake rotors and note detail of 'hot-spots', 'glassing', grooves or discoloration in appearance. Also, do you feel pulsations in the brake pedal while coming to a slightly aggressive yet gradual stop from a highway speed? But, from experience, the upper pan on the old girl is pouring oil at an increasing rate every lube and oil change. Getting new tires usually creates heightened awareness of the vehicle, and that means you just might be smelling a 'familiar' 'new car' type of aroma, even though the concern is not particularly 'new'. If I had to bet my last ticket and flag those hours of diag in the shop, Id honestly place my chips on the catalytic-converter bet. I'm no psychic and more data would yield more detailed methods of diagnosis. However, experience tells me, engine oil leaking faster due to older leaks increasing from higher pressure within the block from more blow-by, while the exhaust is getting more restricted from deteriorating cats, MAP is on the rise, leaks become more aggressive, excess heat due to engine under more load and higher frictions due to heat. All this means more oil is now dripping onto your increasingly hot exhaust. I could, and very well may be entirely and absolutely wrong. I do hope that you find some of the info provided helpful in making decisions regarding your four wheeled friend. :)