I can’t confirm nor deny that a hot shower/bath will cool you down better in hot days. But I can offer some anecdotal knowledge: the feeling of coolness stays slightly longer after a warm shower - like, just a little, enough to be felt warmer than your skin but not hot. Just make sure to quit the bathroom as soon as possible - the coolness comes from the water evaporating from your skin, something not likely to happen in the humidity-filled environment of the bathroom after a hot shower.
Speaking of which, that’s an important caveat on the hot drinks advice: your skin must be able to evaporate sweat for the coolness effect to take place, something hard when humidity is high.
Side note: I just discovered this interesting little device: https://sunscreenr.com/ a cheap and portable UV camera, so you can check on your sunscreen protection.