...although...OP could confirm it by having someone else start it after it's cooled down a bit...like in the a.m.
If you have coolant leaking into cylinders, like I did in my e36, you'll notice it worse when starting in a.m. It'll sputter until it burns off...then the amount leaking is so slight, it's not noticeable...until it gets worse and worse. There are many different fractures possible that can lead to this...just the gasket or in the head (as happened to me).
Debut Radio Show Tues, May 3, 1 p.m. on Hamiltonradio.net The Mechanical Animals
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A recent set--NSFW audio: https://youtu.be/_dcxcZfD6dg
Mangofy your E46!