I think you might be looking to learn, so please forgive me if I have been or am being a bit hard on you.
The overall temperature of the Earth's crust IS affected by additional heat in the atmosphere, but it negligible except at the very surface and even there the additional heat is not enough to melt rock.
Magma comes from
below the Earth's crust. Far below.
The mean temperature of the sea IS changing. It is rising.
If you look at it as a thermodynamic system it doesn't add up,
No, you don't add up. You haven't done the math, not even a back of the envelope calculation.
The trapped heat does heat up the
surface of the crust, down to a few meters. If magma gets that high it is already blowing a volcano whether there are six feet of snow or six feet of humid jungle above it. The trapped "greenhouse" heat does also heat up the oceans.
Study up on the following topics:
Magma reservoirs
Volcano structure
Magma conduits
Melting temperatures of common magmatic rocks
Permafrost melting
Ocean temperature rise
Ocean currents
Heat budget of the atmosphere and the biosphere (which goes down a meter or two generally)
Projected temperature rise expected due to anthropomorphic global warming
Thermodynamic equilibrium
Heat flow
Specific heat content of the atmosphere and oceans and earth's surface considered as a whole.
If the atmosphere warms up 1 degree Celsius (1.8 deg F), then the surface would warm up 1 degree also, and same for the oceans as an average because they are all in contact and thus more or less in equilibrium. They can't rise more than the atmosphere because it is the atmosphere that is raising the temperature. This is a generalization and averaging; some localized changes would be higher and the equilibrium is not perfect, but as a first approximation it is very good.
That 1 degree at the surface does not get magically magnified if it miraculously managed to penetrate 10 meters or a mile or 20 miles (depth of the crust, approximately). It is a maximum. The further it penetrates the more it gets dissipated.
Note about debating tactics: Any time a debater says "So you're saying that ..." they are almost certainly going to be wrong. If you want to have a conversation in which to learn something, then try writing something like "Does this mean that ...".
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