Car Shudders When Brakes Are Applied

From the sound of your problem, this seems more like an engine mechanical problem than a transmission problem.

You noted that your Mazda 3 isn’t heating up and that there is an odd smell, at times. I would look at the cooling system. Specifically, the thermostat is, more than likely, gone and it is allowing the coolant to flow unimpede through the engine. Proper engine operation requires that the anti-freeze/coolant reach a certain temperature before it is released to the cooling system. If the anti-freeze/coolant doesn’t reach the critical temperature then your Mazda 3 won’t operate properly.

Like as not, you will find that your Mazda isn’t getting top mileage, as well. And, its performance, as you indicated, isn’t all that good.

Fortunately, repairing the thermostat is an easy fix because it sits right below system’s pressure cap. Usually, this fix is less than $125.