Does the dew point temperature have to be above a certain value for a thunderstorm?

Only for the special case of thunderstorms coming up from the south in summer. I have seen many thunderstorms (real crackers as well) in April with air temperatures of 8 degC and a dew point of 4 degC. What is really important is that the air must be unstable (see "stable and unstable air masses"), usually achieved by warming at the bottom or by cooling high up or both. Then you need a trigger to release the instability, usually heating and input of moist air (high dew point), but if the air is unstable enough just the heating will do. Other triggers are forced lifting of air over hills or forced lifting by convergence (e.g. sea breezes).

(thanks to Will Hand for this answer)