Sigh. Haven't we been through this before? Baccheus is correct. Heat flow varies a lot from place-to-place across the globe, but the global average is less than 100 milliwatts per square meter. There are lots of global heat flow maps that you can look at, you can see one at this site:
http://geophysics.ou.edu/geomechanics/notes/heatflow/global_heat_flow.htm
Some places like the East Pacific Rise and, apparently, West Antarctica have values substantially higher than 100 miliwatts per square meter; other (larger) regions have substantially lower values. That's how it works out to be less 100 over the entire globe.
More importantly, that's not the number we're interested in for climate change--what really matters is the CHANGE in the heat flux over a few decades, and that is almost certainly several orders of magnitude less than the flux number. Ever been in a mine or cave? If you study the heat diffusion equation you'll find that it takes a long time for a heat signal to propagate through the Earth and it decays as it propagates, so even if you have a very active volcanic year the vast majority of the Earth's surface won't know anything about those volcanoes going off--at least not from changes to the heat flux.
By the way, I'm not saying anything is wrong with measurements in the Advances in Science paper you linked to, in situ measurements are always good reality checks for remote sensing. The heat flux may even be contributing to some ice melt there, but in general geothermal heat flux is an insignificant contributor to global climate change on the time scales we're interested in.
The other "paper" ("Plate Climatology Theory") is by a crackpot who has no idea what he's talking about. He apparently never studied geophysics during his geologic career or he would know that the things he is proposing are not physically reasonable on geophysical bases, much less atmospheric.
Why do you look to crackpots to explain things?
EDIT: To answer JimZ's question " What is about alarmists that cause them to think we know everything already?" Scientists (i.e., what you call "alarmists") don't believe we know everything, but we do know SOME things, and those things put limits on just how much the geothermal flux gradient can be contributing to recent climate change. If you want to understand those sorts of things, I would suggest that you get off your duff and take a graduate class in geophysics. You need to learn about the heat diffusion equation, so it's going to require math at the level of partial differential equations. Then it would help to know the thermal conductivities of various rock types so that you can understand estimates of thermal diffusion times. You also need to learn some geophysical inverse theory, and you need to know about Fourier series and the Nyquist sampling rate. You might want to pick up a standard textbook in geophysics like "Geodynamics" by Turcotte or "Principles of Geophysics" by Sleep and Fujita.
There seems to be a general assumption by JimZ and other non-scientists in here that we really know nothing about the planet, that it's all a big mystery that we can never hope to solve. I can see where you might think that if you haven't studied physics and geophysics. Clarke said "Any sufficiently advanced technology is indistinguishable from magic" and science must seem like magic if you haven't put in the effort to study it. If you DO study it, you'll find that some things are physically reasonable and some things aren't. There are observational limits on global heat flux. It can't just be any value you think it can be and it can't suddenly change from one value to another. This is a big system and there it's been here for 4.5 billion years or so.
What you think of as your "skepticism" is actually just intellectual laziness on your part.
Another EDIT for JimZ's comment on vents: Geothermal vents are very cool (not literally) things. Heat flux is certainly locally much greater if is carried out by convection of water rather than thermal diffusion through rock, but most of the ocean bottom is NOT covered by geothermal vents. Do I know how exactly how much heat is being transmitted through the vents? No, but what I do know is that since the vents make up such a small fraction of the ocean bottom that even if I assign a very large heat flux to any vent and add up all the vents, it's still not going to change the numbers appreciably. That's what you don't seem to get--it's not that scientists know everything, but they can make estimates and determine which things are important and which things aren't. Vents are certainly VERY important locally to the geothermal heat flux, and most of that is probably already reflected in the geothermal flux measurements on ridges, but they're not going to change the global average from 0.075 Watts per square meter to anything close to 1 Watt per square meter. No way no how.
If you think they can, demonstrate it. Make some assumptions on how many vents there are and what their water flux is and how much their outflow is greater than that of the ambient water, then we can compare the energy in those vents with the energy flux from the rest of the ocean bottom. I'm going to put my money on the rest of the ocean beating the vents hands down.
And what's more, again it's not the geothermal heat flux that matters, it's the variability of the geothermal heat flux, which as I said before is almost certainly several orders of magnitude lower than the flux itself.
Again, you don't have to know everything, but you pretend that scientists (and I'm not including you because you seem to have no interest in actual science) don't know anything, just because you don't.