Here, we report the effect of reduction in particle size on the temperature dependent magnetization of chemically synthesized BiFeO3 nanocrystals with average grain size of 55 nm. The X-ray photoelectron spectroscopy results show a significant broadening of binding energy peaks associated to Fe3+ 2p3/2 core levels due to the reduced size. Additionally, due to the nanosize effect, the M-H loops show a significant coercivity starting from 390 K with an anomaly located in the vicinity of 150 K in our Hc vs T as well as Mr/Ms(50 kOe) vs T curves. At this temperature, both Hc and Mr/M s(50 kOe) undergo minima. Additionally, our results for the first time show the evidence of existence of a low temperature anomaly due to spin-glass transition in the range from 40-44 K in the field cooled magnetization curves. In bulk single crystals, this transition is reported to be situated at around 50 K, however, this transition remained so far undiscovered in the recent studies on BiFeO3 nanoparticles due to the insufficient temperature resolution. The significant shift in this transition toward lower temperature can be attributed to size dependent effects. Our results clearly present new information on the size dependent properties of BiFeO3 nanoparticles.