I am not sure, I doubt if the central limit theorem deals with hetero. Although it is possible that large sample sizes might for other reasons. But generally if you are worried about it White standard errors is a good idea. None of the solutions that I have heard for hetero are easy to do other than modifying the SE. If you are new to statistics I doubt you will want to do the other solutions.
from wikipedia
"
Under certain assumptions, the OLS estimator has a normal
asymptotic distribution when properly normalized and centered (even when the data does not come from a
normal distribution). This result is used to justify using a normal distribution, or a
chi square distribution (depending on how the
test statistic is calculated), when conducting a
hypothesis test. This holds even under heteroscedasticity. More precisely, the OLS estimator in the presence of heteroscedasticity is asymptotically normal, when properly normalized and centered, with a variance-covariance
matrix that differs from the case of homoscedasticity. In 1980, White proposed a
consistent estimator for the variance-covariance matrix of the asymptotic distribution of the OLS estimator.
[3] This validates the use of hypothesis testing using OLS estimators and White's variance-covariance estimator under heteroscedasticity."
