We report on precise low-temperature specific-heat measurements, C(T), of YbRh2Si2 in the vicinity of the antiferromagnetic phase transition on a single crystal of superior quality (residual resistivity ratio of approximately 150). We observe a very sharp peak at T_{N}=72 mK with absolute values as high as C/T=8 J/mol K2. A detailed analysis of the critical exponent alpha around T_{N} reveals alpha=0.38 which differs significantly from those of the conventional universality classes in the Ginzburg-Landau theory, where alpha< or =0.11. Thermal-expansion measurements corroborate this large positive critical exponent. These results provide insight into the nature of the critical magnetic fluctuations at a temperature-driven phase transition close to a quantum critical point.