The fact is, I'm a nerd who looks like Shrek and smells twice as bad. As such, I'm always shooting for good mpg (like a nerd). My average on here is something like 42 or 43 maybe. And with such an average, I crank and go. I'm turning off the engine as it rolls to a stop in its parking spot or as soon as I can get my hand on the key after parking. Even with it warm outside, I put the 2 left side windows down, and throttle cross-breeze with the front RH window. Meaning I hardly ever use the A/C. When it is 95° or warmer outside, then I'll use the A/C. But I really enjoy the breeze and don't mind being warm. So I'm trying my darndest for mpg.
That said, I don't think you're numbers are all that low, for a CVT vehicle. Considering your usage. As for a cold CVT, it probably wouldn't be the best thing for your good ole CVT to push your car with a cold engine / cold cvt car to the start line of a drag strip and then try to set a sub-18 second rip-roaring-blast down a dragstrip right when it is cranked up. But I don't believe it would hurt a thing to crank and 2 seconds later be gently pulling away from your home or place of bidness and driving easy for the first 30 seconds or so.
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View my fuel log 2020 Mirage ES 1.2 manual: 42.4 mpg (US) ... 18.0 km/L ... 5.5 L/100 km ... 51.0 mpg (Imp)