The standard way to melt icebergs would have been entirely possible with 1940s technology.
It's as simple as it's effective - high pressure seawater. Very, very effective (high specific heat content, salt, almost trivial cost of deployment and inexhaustible). Low cost of deploying multiple of them, as well.
You do not want to be using flamethrowers or lasers and similar on sizeable icebergs or coastal ice buildups - they may be great for some things, but hopelessly outclassed in this job, for sheer ease, speed and efficiency, by high volume water cannons. You can also forget blowing them up or destroying them with incendiaries (thermite) - the US Coastguard already tried that idea in 1959/1960 and it failed (report + photos).
(Just in case you wondered, no, you don't need to heat the water. Its high specific heat capacity means even at arctic sea temperatures, it already contains a lot of low grade heat energy, and will do quite well at melting ice in bulk. Also, freezing takes energy, and the energy it would take to freeze salty seawater from a few degrees above 0C/32F is enough that given a strong flow, the ice will readily be melted, or cut through, instead. Just make sure to use high pressures/volumes - ideal equipment would be very large bore fire-hose and powerful high-volume high-pressure seawater pumps.)
The mechanics of melting with seawater are deceptively simple. You aren't limited in the amount of water used, and pumping is relatively cheap, so you don't need to melt a lot of ice per unit of seawater, to eventually have a significant effect. You can be persistent - eventually it can't help but work. The pressure, dynamics, and salt will help. (Pressure works small fractures and pits into large ones and speeds up penetration; dynamics such as massive turbulence and huge ultra-fast-flowing torrents/runoffs will cut into the ice; salt tends to reduce re-freezing and hence increase runoff). But even those aren't essential factors. Time - and at least some heat transfer on a bulk scale - will do it.
Is this practical at scale? For a sense of "what scale is possible", check out this diesel pump built in Mississippi around 2011, at 150,000 gallons a second = one Olympic swimming pool every 4 seconds. Could they do that in the 1940s? Probably, look at other huge engineering projects, steam ships, and so on, of the 19th and 20th centuries. Or if not exactly, then enough to deal with a lot of ice at least. Nothing in this says to me that they couldn't have done something similar on the 1940s, if they'd wanted, or close enough to have a similar effect.
For huge 'bergs, as the ice becomes cut up, the smaller bergs also become easier to separate, ending the cold microclimate that surrounds huge 'bergs, and making them more vulnerable to being tugged, pushed away (again with water jets), and exposing more surface to the sea/air/pressure hoses.
There's no reason this couldn't also be used with coastal and continental ice as well as floating ice, if it's either relatively close to the coast, or one can drill through it to seawater.