There is no evidence that taking a hot bath can cause a miscarriage in early pregnancy. In fact, there is some evidence to suggest that exposure to heat during pregnancy can actually be beneficial.
One study found that women who took at least one hot bath per week during their first trimester had a lower risk of miscarrying than those who didn't take any hot baths. Another study found that pregnant women who used a sauna four or more times per week were also less likely to miscarry.
So while there is no need to avoid hot baths altogether, it's probably best to limit your exposure to very high temperatures. And as always, consult with your healthcare provider if you have any concerns about your pregnancy.