In my home growing up we raised Himalayan cats. From my experience, the males do not go through a time of "heat", but once they start wanting a female, they never stop. Females do have a short period of heat, but males are like men and just want it all the time. Unfortunately my male cat I have now was fixed when he was just a few months old, but still acted like a male does when he grew up. He started mounting my female cat, who before then had pretended to be his mom. She was not at all happy that he wanted his "mom" to be his "girlfriend". I felt so bad for her because she loved playing mommy. He's never been great about making it in the litter box. He does some time and sometimes not. When he was young I thought he just preferred a pristine kitty box, but then he had to have surgery for a stone in his bladder, so I thought it was that. Now I just think he's just lazy or something. I don't know. I do feel like females are better about making it in the box. I'm sorry if I'm not giving you good news. Some people have better luck with their males, but I've regretted getting a male since the beginning. I would never, ever give away my Happy, but I just wish we had gotten his sister.
My only advice would be to get him neutered asap! Well, and also figure out if it's behavioral or physical (if it continues past his neuter time)- your vet can help to determine that. My male has obviously had bouts of both.