Usually, no. Everything expands with heat so, naturally, everything contracts when cold. As a result, even cold, thick oil can ecsape past worn rings & get burnt in the combustion chamber creating blue smoke. As the engine warms up, the rings, piston & bore expand creating a tighter fit & the oil thins out making it easier to be scraped away by the rings. Some oil will still get past but, not as much.
You have the opposite problem, the blue smoke is appearing once the engine is warm. The reason for that is as the engine heats up, so does the oil &, like everything else, it expands as well as thinning out.
There are three rings in a 4 stroke set, 2 compression rings & an oil ring, The oil ring is designed to scrape excess oil back down the bore into the crankcase but, it can only do so much. If there is an excess of oil in the crankcase, more will be splashed up the bore, the oil ring will scrape away most of it but, will still leave an excess which is then scraped up into the combustion chamber by the compression rings & burned, creating blue smoke