Hi Nathan, I'm not sure that sulfuric acid will even react with methyl benzoate by itself, at least at room temperature. I'm assuming this experiment is the nitration of methyl benzoate using HNO3 with H2SO4 as the catalyst (to generate nitronium ion, NO2+, the actual electrophile in the reaction). The mononitrated product is methyl 3-nitrobenzoate. I suppose one possibility is sulfonation. Sulfonations with concentrated H2SO4 alone (without SO3) can be done when a ring activating group is present, but heating may still be required. Toluene can be sulfonated this way by boiling a mixture of toluene and H2SO4. But methyl benzoate will be much less reactive, with the ring deactivating ester group present, so it seems unlikely that sulfonation would occur. I've not heard of any problems with the ester group reacting with conc. H2SO4 either.
I've seen some procedures for this reaction that do not require cooling the H2SO4 when mixing it with methyl benzoate, especially if small quantities are used. However, it is important for the mixture to be cold before adding the concentrated nitric acid, otherwise, the heat from mixing the acids and/or the heat from the nitration of the ring itself provide sufficient energy for the less-favorable dinitrated product methyl 3,5-dinitrobenzoate to form. This is a general problem that requires careful control of the temperature in all aromatic nitrations.
Steve