This is quite an old question, so I hope it's ok that I try to answer it (I just stumbled onto it doing other research and I think I can help).
See, the PETM was not a "mysterious" rise in temperature, instead it was linked to volcanic activity in the Atlantic. The whole warming of 5 to 8°C over 20,000 to 50,000 years was linked to the massive amounts of CO2 and other carbon gases (like methane). The estimate is at around 12,000 billion tonnes of carbon over the entire duration of the release (averaging at 0.24 GtC a year — also sometimes written as PgC for petagram of carbon). That's equivalent to around 44,000 gigatonnes of CO2 (the IPCC report gives 3.667 tonnes of CO2 for every ton of carbon). For comparison, humans are currently emitting about about 50 billion tonnes of CO2 a year (around 13.6 PgC), and since 1751 we have accumulated around 1.5 trillion tonnes of CO2 (or 1,500 gigatonnes, 1.5 exagrams or 1500 Pg, so 410 PgC — roughly 12.5% of the PETM amount). So in a way the PETM can be compared to anthropogenic climate change, which, although so far smaller in overall carbon releases, is much (much) faster.
Now, if this phenomenon had continued in the early Eocene, presumably, yes, the warming would have been more significant. There is considerable carbon stored in the Earth's mantle, and prolonged volcanic activity could have released more, however with the way plate tectonics works, it was bound to stop at some point.
It should be noted, however, that although the PETM is associated with a peak that falls back to the pre-PETM levels in a matter of a few hundred thousand years (relatively short over geological periods) the global temperature did slowly increase back to a level that equalled and maybe even surpassed the peak of the PETM during the Eocene optimum, which, depending on definitions, lasted from 2 million years (53 Mya to 51 mya) to roughly the extent of the Ypresian.
Source: Robert A. Rohde through [Wikimedia]
So overall, even if the PETM did seem like a brief and extreme increase in temperature, you can see that this rapid warming (called a hyperthermal, and there were probably more) was part of a global trend that peaked only 5 million years later. So in a way, the warming did continue. Also, even if starting around 51 Mya the climate started cooling slowly, the whole of the Eocene remained warm compared to the modern-day (at the end of the Eocene, rapid cooling led to an extinction event that marks the end of that period, and is thought to be due to several factor, like the formation of a circular current around the Antarctic and asteroid impacts in Russia and Chesapeake bay).
But if your question is: could I handwave things and make a world where the carbon release from volcanic sources continues for half a million years instead of roughly 50,000, then I guess you could just say "eeh it happens" and not bother with the details, extrapolate the increase in carbon (using the 0.24 GtC/yr and possibly the conversion to CO2eq by multiplying by 3.667) and looking up how to calculate the impact of that level of CO2 on the climate (although some studies attribute the warming to seabed methane and that wouldn't affect the CO2 level). You'd have to look at Global warming potential and deal with equations that honestly are beyond my level (and make sure that the type of carbon you're dealing with fits with what you're calculating).
But yeah, overall, if you want a comparison with volcanic activity at plate boundaries happening for an extended period of time, look at the Permian-Triassic extinction
If you want a quick idea of what it looked like, this tumblr post goes into some interesting detail.
Hope this helps!