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We go to Tulum every year in August - then, it is brutally hot.
Late May-June shouldn't be too bad. Keep in mind, June is the rainiest month.
Don't know about Belize.
"hot" is always a relative term..... May and June high 80's/low 90's and July definately in 90's but with the ocean breeze I find it alright but I'm used to hot/humid in summertime.