I was wondering is it normal to feel tooth sensitivity if you drink hot then cold water afterwards?

Not necessarily: Temperature sensitivity of teeth can be a harbinger of underlying problems.

Temp Sensitivity: It is very common to get temperature sensitivity if you are a clencher or grinder of your teeth you can get wear facets that are thinning of the enamel which can actually break through the enamel. Recession of the gums may cause root sensitivity. It may be an omen of a bigger problem i would discuss the situation with your dentist to determine if treatment is necessary.