A 9V battery typically doesn't have a very high current capability. Probably not any more than about 200mA, possibly more if it is fresh, but it won't last long. They basically consist of 6x AAAA-size alkaline batteries in series, so they don't have a lot of capacity.
Anyway, the Test Load will get hot with use, which is expected with any type of rectifier when you're passing that kind of current. But, I don't see any reason why it would be the cause of a low reading unless something wasn't right. Meter set to measure voltage? The setting pads were properly bridged? Measure voltage across the two thru-hole pads on either side of the larger resistor marked "1R00"?
To me, I would guess it was the 9V battery giving you low readings, but if you say it was putting out a correct current when you were directly measuring current with the multimeter, that seems to rule it out to me.