Other than newly deep baked charcoal finished oolongs, such as Tieguanyin, and the subcategory of puer (shu cha), black tea in generally maybe the least cooling in TCM nature amongst all teas. However, that does not mean that it is hot and should be avoided by people with a “hot constitution”.
3 times a week is not an issue providing that you have real leaf tea, and those that are relatively fresh (so not stored for a few years) and wholeleaf. CTC (the way broken leaves are manufactured) so considerably alters the TCM nature of tea that most knowledgeable Chinese TCM doctors classify teas made through it not as “hot” but rather “dampness-toxic”. As such, CTC black teas are not good for you. Since the heat toxic in your system would combine with the “dampness” to become “dampness-heat-evil” (in the exact term of TCM translated) which is one major pathogenic energy in TCM term.
Tea in general is “cooling” by nature, esp green, white, and oolongs. They will help your heat excess. Do not have them cold and too strong. Avoid using sugar and milk, if so, fresh whole leaf black tea is also good. Overall, choose the right teas and have 5 ~ 8 cups of tea a day to see the effect on helping you to balance your heat.
Good health.