Retired US nuclear submariner here, having served on three attack boats, and having surfaced under the polar ice cap. Hence a few notes:
As stated, diesel boats were not built for under ice ops, the most limiting item being the diesel engine's need for lots of air, requiring frequent surfacing to gulp said air, and the inherent power (read: distance) limits of running on batteries. If you can't surface frequently, you can't go under the ice.
Also, as stated, you would not use heated water from the propulsion plant to melt ice to surface - dumb on many levels, and not worth disclaiming.
Most, but not all, US Nuclear submarines have hardened sails built to withstand breaking through the ice. This includes being hard enough to break through several feet of ice without being damaged, and also includes the ability to retract the many items that stick up through the sail (e.g., periscopes and antennae) to prevent their being damaged.
Regarding the hardness of the sail, consider that the hull of the submarine can withstand submergence pressure at over several hundred feet, so ice hardening of the sail is not a significant challenge, you just design it in.
Now, how to surface: Using upwards facing telemetry, you watch for thin places in the ice, not that it matters for more than convenience, and to protect the ship's screw or propulsor. These thin spots are called "polynyas". When you find a good one, you just go "ice pick" it, going dead slow, and let your sail top come to rest on it. It typically takes a slightly positively buoyant condition to ice pick, and you want the boat trimmed out level.
Then you do a main ballast tank (MBT) blow for a few seconds enough to become positively buoyant enough to crack the ice slowly - there is no need to waste MBT air bank air, or to "pop" up. The sail will easily crack through the ice, given that a boat has sufficient MBT volume to create several hundred tons of positive bouyancy, and that the sail is a good fulcrum.
I hope this helps.
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