Rusty:
I agree with Kennyd and Ron, except that I would strenthen Kennyd's "definite maybe" to a "definite probably will work" as a heat exchanger because in a logsplitter by design the pump will be working hard at most one-half the time (when the wedge is being forced through the log). The pump is not working very hard when the wedge is retracting, and it is working hardly at all when the wedge is stationary. Furthermore, you are not likely to run the splitter for hours on end at the maximum pace (unless you have a lot more stamina than the rest of us).
I think the rule of thumb of one gallon of reservoir per gallon per minute of pump sorta/kinda assumes a pump working full time at near maximum pressure, hence the heat generated from pump losses will be much greater than if the pump were working only part of the time.
There is a consideration other than oil temperature. Exhaust oil may/will have both entrained air bubbles and debris, despite the fact that it just passed through a return filter. A larger reservoir allows the return oil to linger in the reservoir longer before it returns to the pump, and the oil in the reservoir is relatively less active. This additional rest time allows the air bubbles to escape the oil and allows the debris to settle to the bottom of the reservoir where it is removed when the oil is changed.
I assume your pump is a gear pump, and they are less sensitive to oil condition (cleanliness, air entrapment) than most other pump types.
If a 15 gallon tank is available, not much more expensive than a 10 gallon one, and fits your splitter, I would get it. Otherwise I would use a 10 gallon tank with temperature guage and quality breather cap (no larger than 40 micron), install a good 10 micron absolute rated (not nominal) return filter with bypass valve (30-40psi) and pressure gauge, and use a quality fluid like Kubota UDT or super UDT or John Deere Hydraulic/Transmission fluid. I'll wager (not much) that the oil temperature never exceeds 190 deg F.