Here's the issue in a nutshell.
A change in net energy of a geologically relevant magnitude is going to have geologically relevant (meaning, seemingly massive, strange, or radical, from our very limited perspective) affect. Particularly since the earth right now is (or has been) relatively stabilized by the presence of massive amounts of ice and permafrost, and a very high surface albedo.
In fact, back when total atmospheric greenhouse molecules (most constituents of the atmosphere, which are not the atomic gases (02, N2, Ar) that make up most of the atmosphere, are greenhouse gases) and which are most non noble gas molecules in the air by the way) were as high as they have just reached, oceans, ultimately, were a couple to several dozen meters higher.
It could be a coincidence, but it's probably not. There is a LOT of permafrost, which isn't all that far away, temperature change wise, from melting.(Some of it is slowly starting to.) And the tundra underneath this white layer has a far lower albedo, which would mean far less visible light - which is largely not absorbed by greenhouse gases - would be reflected back off the surface of the earth rather than absorbed as retained heat energy. (Which would then be subsequently emitted as thermal radiation, which with its far higher and broader wavelength than the very narrow range that solar radiation consists of, is absorbed by greenhouse gases, and re radiated.) Melting snow, though it still has a very high albedo relative to open tundra (or even forest), also has a significantly lower albedo than frozen snow.
All of the "permament" sea ice in the northern and southern latitudes, which if course is not permanent at all, also has an exceedingly high albedo. Open ocean water, which is what it turns into when that ice melts (or, rather, overall average ice coverage declines) has an extremely low albedo,and instead of reflecting back most of the sun's heat, absorbs most of it, instead. A radical difference.
In addition, there also happens to be about a trillion tons of carbon buried in the permafrost, about twice the total amount currently in the atmosphere (which itself, again, not taking into account the further exacerbating heightened atmospheric levels of a few other key greenhouse gases, most notably methane, is higher than it has been in at least two million years). Not all of it would of course be a net addition to the atmosphere, but only reflect an adjustment to the overall carbon cycle - like all net additions - leaving a lot of excess in the atmosphere. But it would be a remarkable contribution.
More significantly even, much of that carbon would be released in the form of CH4 or methane. Which is several hundred times more effective at trapping and re radiating heat as methane than is CO2. (Which is what over several years methane starts to break down into. You'll also often hear how methane is "24" times as potent a greenhouse gas as carbon dioxide, or "100 times" or something such. Most of the time, when correctly written, this will also reflect a time period. This is because methane breaks down into carbon dioxide, but not all "at once and on a set schedule." So the overall re-radiating affect comes from a combination of the gas as both methane and carbon dioxide, which, the longer the time period, the more skewed toward carbon dioxide's lower heat trapping response, and thus the lower the overall potential in relation to carbon dioxide.)
In terms of really radical changes to albedo and most of the permafrost trapped carbon, it may take a little while - large ice systems are pretty stable. But as a matter of basic physics (further corroborated by what the world was like the last time levels of atmospheric greenhouse gases were this high) they will change. How much, minor or major, depends on what we can't know or control - and that is simply whatever the precise range of this wild whole earth experiment will be. And far more relevantly, on what we can - how much we continue to add or not add to the atmosphere, or even ameliorate.
A shift in total otherwise outgoing but instead re radiated heat energy - even if over the last few hundred, or even the last several thousand years it is not directly off of the lowest levels of the past several million years - that is nevertheless greater than the earth has seen in several million years (back to a point when the oceans ultimately were some 30 to 60 some feet higher, meaningless in earth terms, very meaningful to us), is a geologically monumental event from the perspective of the geological conditions that have existed on earth over the past few million years. (Namely, our perspective). And the most basic thing being overlooked.
GG gases do absorb and then re radiate ("trap") heat. It's not an option for them. That heat energy has to go somewhere. Heat doesn't just "disappear," unless it goes into outer space. And the whole reason why more gg gases (in an atmosphere still only consists of a very small fraction of them) is relevant - the same reason why the earth is not a frozen ball to begin with - is that these gg gases reduce the amount of heat energy lost back to outer space.
It may seem hidden for a while, as the changes at first seem minor, and then as those ("minor") changes (a fraction less ambient sea ice, a tiny decrease in frozen permafrost), slowly drive a little more - which would otherwise be near meaningless. But here those changes are being combined with the fact that the earth, due to multi million year high levels of long lived atmospheric gases coincident to our enormous if inadvertent dumping of them into the atmosphere, is now also trapping and re radiating much more thermal radiation (given off by the earth's surface) than it has in millions of years: Slightly warming the atmosphere, and adding to the buildup of energy (most easily notable in oceans, in which just slight temperature variations represent an enormous shift in energy), at the same time, furthering the changing process from a more (long term) stabilized high ice coverage very low ocean high albedo to a different, higher earth net solar radiation retaining stases.
It is not a shift from less heat to more heat being trapped in an atmosphere which then as a result will add to temperature a little bit, as the constant and incorrect conflation of current conditions to the current level of the problem, suggest, and which most people on some level seen to still intuitively believe.