Hi Nathan, when you mix pure sulfuric acid with concentrated nitric acid (about 70% HNO3 in water), you are diluting the H2SO4 just as if you were mixing it with water, which, you'll recall, is a very exothermic process in which a weakly-held hydogen ion from H2SO4 is transferred to a water molecule, forming hydronium ion, H3O+. Thus the old rule, "Add Acid" for sulfuric acid, meaning you should slowly add the acid to the water instead of the water to the acid, to help prevent the danger of sudden boiling and splattering of hot acid. Keeping things cool helps prevent this overheating.
If you are mixing only a few milliliters of concentrated H2SO4 and HNO3, the amount of heat released will not be so great, so a water bath at room temperature is normally adequate to ensure that overheating does not occur. You can even do the mixing in a small graduated cylinder with no water bath. But larger volumes are often mixed at ice bath temperatures just to be on the safe side.
Aromatic nitrations easily result in "over-nitration" to form dinitrated products and/or decomposition products if the reaction gets out of hand. This problem is lessened if the reaction is done at lower temperature. Nitrations are also exothermic reactions, so in the absence of a cold water bath, the increase in temperature could cause the reaction to get out of control.
It may not be necessary to chill the methylbezoate when adding only H2SO4, but if there are impurities present that could react exothermically, doing the mixing at low temperature would help prevent possible sudden overheating and dangerous splattering of hot acid. In fact, whenever concentrated sulfuric acid is used, it is a good idea to do all mixing in a cold water bath or ice bath, adding the acid dropwise with continuous stirring.
Hope this answers your question, and welcome to the group!
Steve