That is a real problem. While conditions, reagents, and reactants can be used to predict which it will be, but as you have pointed out, this is a reaction in which it biased away from one of those definitive reactions. If someone actually had real data, that would be useful. For example, if rather than just 2-butanol, it was (R)-2-butanol and the product of this reaction were given, such as (S)- or racemic 2-bromobutane.
So, let me draw from reactions I know. I agree with 1-bromobutane. That reaction is also heated, so just mixing them together probably isn't working. If it were a simple SN2 reaction, the rate might be slow, but it should still go. The higher the reaction is heated, the more likely the activation energy of other reactions might also be overcome. If cyclohexanol is heated with phosphoric acid, there is a very fast protonation reaction that takes place and then supposedly loss of water to the carbocation. This loses a proton to give cyclohexene. Because it is heated, I am going to guess that butene is also going to form. Since these are not good E2 reaction conditions, elimination is probably an E1 reaction. Therefore I am going to go with SN1 as the reaction mechanism.