We study the behaviors of mean end-to-end distance and specific heat of a two-dimensional intrinsically curved semiflexible biopolymer with a hard-core excluded volume interaction.We find the mean square end-to-end distance R2N ∝ Nβ at large N,with N being the number of monomers.Both β and proportional constant are dependent on the reduced bending rigidity κ and intrinsic curvature c.The larger the c,the smaller the proportional constant,and 1.5 ≥ β ≥ 1.Up to a moderate κ =κc,or down to a moderate temperature T =Tc,β =1.5,the same as that of a self-avoiding random walk,and the larger the intrinsic curvature,the smaller the κc.However,at a large κ or a low temperature,β is close to 1,and the conformation of the biopolymer can be more compact than that of a random walk.There is an intermediate regime with 1.5 ＞ β ＞ 1 and the transition from β =1.5 to β =1 is smooth.The specific heat of the system increases smoothly with increasing κ or there is no peak in the specific heat.Therefore,a nonvanishing intrinsic curvature seriously affects the thermal properties of a semiflexible biopolymer,but there is no phase transition in the system.