Overcharged does affect the heat handling - look at the "heat efficiency" stat of the reactor. A rated default will be 0.4, G5 overcharged increases this to 0.5. With thermal spread experimental applied, it will be 0.45.
So, technically the thermal load remains the same, the reactor is just less efficient at dispersing it through the heat vents/creates more heat for the same work (one of those two, at least, if not both).
Well... no. Not really. It's just my own observations from playing and some things I recall from reading elsewhere about what the "heat efficiency" stat actually means (it seems to be relative to the power generation, eg an efficiency rating of 1 means it produces... for lack of better wording to use, 1 "unit" of heat per 1 MW generated, while A rated reduces this quite a bit).
Of course, there are distinctions to be made between how each ship handles heat individually, but that's too complicated and better explained in a thread which did detailed heat mechanic research (link not at hand). For your case, you could notice this with a ship's idle heat already, aka just sitting in space with hardpoints retracted and doing nothing. It will 'rest' at a higher level with a default A rated reactor compared to one which has been overcharge engineered. Hence the heat will rise to a higher level when you've got the FSD charging. (And some ships are so bad they are outright at risk of overheating just by using the FSD, but I don't think the T8 is one of those.)
First post explaination in short, its very nice summary how it works, but in nutshell its bit more complex. (its preety straightfoward once one learns how it works)
Basically, "heat efficent" stat is at first glance, is thats how well ship handles heat, be it resting heat, and how fast extra heat is dispersed, in other words, how quickly ship can "cooldown", but thats not all, there is lot more in book that it might look at first glance....
But one thing to note, and its true for most ships (save for few only), say if powerplant its like 0.32, the resting heat will be around at 30%, if its 0.40, then 40% resting heat and if like 0.17, then it can be around 20% or even lower, but that in end depend on ship itself; dolphin dont have high heat capacity but its still one of "coldest" ships by default, while DB series of ships have very high "Heat" capacity so those 3 are top at heat game.
Lower "heat efficenty" stat is, it means less heat generated per each MW that modules uses, as more MW is used, ship get hotter. It also disperses heat quicker per second but cap is I think at 7% per sec.
One of ways to make ship run "cooler" is to lower MW usage; either turn off unneeded modules if not needed (things like cargo hatch, FSD during normal flight mode etc) or/and engineer specifically for lower MW usage and heat gain (clean drives say hello - but its not recomended in PVP - clean drives are like 30% slower) apart of obvious LE power plant with thermal spread... but note that LE especially in higher grades, are low on MW provide, it takes specialized bulids to correctly utilize such, while OC is required to every Meta bulids in PVP (Full PA FDL - prismatics + 6 A boosters alone its tons of power needed) ... for PVE and rest, a good compromise is using armoured powerplant with thermal spread... its good balance with MW provided by plant and heat handling, and as bonus, its intergrity way more higher, and in some PVP bulids, its required to use such (hull tanks/hybrids bulids say hello)
Of course, since every ship have own heat "capacity" and "bulid in" heat handling and like cases as in T-7, for ship of its size, its heat capacity its quite small and its "heat handing" is one of worst, so it can cry for "heat critical" often, even while FSD charging.
There is thread:
https://forums.frontier.co.uk/threads/research-detailed-heat-mechanics.286628/
Its good and accurate, and more details are there.