Based on your last paragraph, where you've asked for Maths - should this be tagged with the 'Hard Science' tag?

@TheDemonLord I think is one of those questions that's on the borderline of needing that tag but could be answered without it. An answer showing its math would be helpful but isn't necessary, IMO.

@AlexP Although I understand diamond>crust heat transfer cannot surpass mantle>diamond heat transfer, wouldn't convection currents cause cooled-off mantle to "drop off" the bottom of the diamond while hotter rock rises and comes into contact with it? There wouldn't be a "layer of mantle rock" next to the diamond, because the rock next to it would constantly cool and sink. If nothing else, I think the convection currents caused by this constant "radiator" effect would have notable consequences on the surface.

It will not have a noticeable effect, the diamonds will not be pure, and the cooling effect of the atmosphere stays the same, but most importantly the thermal conductivity of diamond drops drastically the closer you get to the temperature of the mantle. It might be slightly warmer, more importantly it will never stay solid the diamond will b broken into fragments under the forces of mountain building.

@John I doubt its thermal conductivity approaches the crust's, even at the temperatures here; I'm assuming at least 100 W/m/K even at 1400 K. Also, the atmosphere isn't relevant to this; as in the drawing, there's a multi-km-deep sheet of poorly-conducting earth/rock atop the diamond that heat must penetrate to reach the atmosphere. I chose diamond specifically because it's good at forming monolithic structures which don't collapse under their own weight; if granite can survive mountain formation, why would diamond "fracture" under the same conditions?

Since it's roughly 50% more dense than ordinary crust rock, it will gradually sink. The much more interesting results will be due to that rather than the differing thermal properties. It will leave a rather interesting trail.

It's a darned shame for this forum that WillK isn't active here any more.

@BobaFit It has sunk to some extent, but it isn't as dense as the mantle, so it "floats" in the mantle like an iceberg. Some of it protrudes upwards into the crust. A portion of what protrudes into the crust protrudes above sea level. The force of the diamond's weight and the weight of the crust above the diamond are enough to "sink" the diamond to some extent, but not enough to make it irrelevant to the question. Also, it's not "roughly 50% more dense than ordinary crust rock"; the crust is 3150 kg/m^3 and the diamond is 3300 kg/m^3.

IMO, there's not enough info here to answer your question. The crust can be 3-43 miles thick. For all intent and purpose, the diamond is an indestructible theremal conductor, meaning the temperature on the upper surface is equal to the temperature on the lower surface. If the crust is 3 miles thick and geological time has past, it's likely that it's "melted off." If it's thicker, you might get a magma chamber, but there's no pressure, so no volcano (much less a supervolcano). Is this next to a large lake or ocean? Then you'll get hot springs and steam vents. Not near? No springs or vents.

Diamond is 3.5 g/cm^3. Crust is about 2.6. The diamond will not stay sticking-up. It will flatten out and spread under the crust. It's not going to float like an ice berg. It will spread like melting wax.

@BobaFit I don't think density is enough to conclude that. The melting point of diamond is about 4000°C. The OP's stated condition is only 1127°C. I don't believe that's hot enough to materially soften diamond - but I could be wrong.

The more I think about it, assuming the diamond mountain really could be believed to float, the result would be a diamond surface exposed to the sky. The crust would be constantly melting off of it. The climate around the area would be interesting, but you would end up with a moat (not a sea) of molten lava around the diamond mountain. The crust can't build up fast enough for anything else. Now, what the mantle would do around the perimeter of the diamond mountain... that's a good question. It's only a guess, but the word "percolate" comes to mind.

Note that so long as the density of the diamond is greater than the density of the mantle, over geological time, the diamond will always sink.

@BobaFit This is not Earth. The crust is 3.15 g/cm^3, because it's made of other stuff than Earth's crust. Maybe the diamond is 3.5 g/cm^3, if that's the only density diamond can be at, but it's still not as dense as the mantle.

@JBH "A magma chamber without pressure" like what you said is what I want; it allows for relatively high surface heat fluxes, allowing things like hot springs, geothermal power, melted or at least shallower permafrost, etc.). The diamond isn't as dense as the mantle, albeit close (~3.5 g/cm^3 diamond, 3.6 g/cm^3 mantle); this isn't Earth, the mantle is different. If the crust constantly melted off the diamond, wouldn't the constant lava flows build the crust up thick enough that it wouldn't melt for long enough to creep over the diamond?

@JBH Basically, think of it as a shield volcano, except, instead of the magma coming out of the peak, it's formed on the sides, by crust constantly being pushed into the relatively hot diamond and then melted back down the flanks.

Ooops, I misread the crust density for the mantle density. Sorry about that. I'm still worried about the geological timelines. Any crust over the diamond would simply slough off. I don't think you'd get a shield volcano. At a guess, you'd get a moat around a whomping hot diamond that would generate fearsome storms about 50 klicks away.

Let us continue this discussion in chat.

When comparing close density values, remember that the density of the mantle is often an average. There can be both positive and negative variations from that average which can either push up a mountain or pull down a basin.

Granite does not survive mountain building intact it is quickly broken into many many units. Look up thrust faulting. Its not weight breaking it it is the forces that thrust it up into a mountain in the first place. at 1000k the thermal conductivity of diamond is around 10 W/cm/K the mantle is around 1200k. That's comparable to the thermal conductivity of quartz.

@jbh melting point is not the same as the temperature at which it will undergo plastic deformation. this is why rock well below its melting point will also deform and flow.

For comparison the thermal conductivity of basalt at the same temperature is 8 W/cm/K the thermal conductivity of some volcanic rocks actually rises with temperature in those ranges.

like I said it may be slightly warmer but not significantly.