What about buying a heat gun and using that as a means to apply localized heat to the suspected chip/solder only? Also you don’t expose your oven (future foods) to the metals in the board
. HF has a basic two temp unit for $15.00.
Amazing deals on this 1500 Watt Dual Temp Heat Gun (700°/1000°) at Harbor Freight. Quality tools & low prices.
www.harborfreight.com
Conversely if you do need to heat up the entire board at any point, a cheap toaster oven works great. I scored a freebie off CL that lives in my garage workshop for these sorts of uses.
If the "oven-trick" at 140°C get's the GPU-problem temporarily fixed, then it's the faulty GPU itself and applying more heat has no more benefit, but may harm the board or other soldered on components, e.g. RAM-benches etc by melting plastic parts or make sensitive plastic brittle.
So 10 min at 140°C would be the first approach. It wouldn't set off toxic fumes: 140°C is below melting point of even lead-based solder and also below the temperature, where fumes were set of from "boiling" flux. So I'm sure, there are no hazards to use an oven for that procedure.
If the oven-trick should fix the problem: enjoy! and take care to avoid future exceeding system-temperatures. (As for the Early-intel MBP's only a GPU upgrade is ultimately solving the problem.)
If the oven-trick at 140°C fails, then it might be a problem of "broken" solder between GPU/BGA and logic-board and you'll need same procedures as for a full-GPU-replacement: pre-heating the board to 150°C, then applying well dosed "heat" to the GPU (combined with flux, to treat oxidation) up to the melting point of the solder-balls of the BGA to "reflow" the solder.
I wouldn't recommend to do that with a heat-gun and without pre-heating the board, because the result is a gamble.
(Honestly, I haven't done any soldering yet - but I'm keen to give it a try, as soon, as there will be spare time ...)