[NewRenter5]

I just moved to a new residence - a ranch style house built in the 80's. The bathroom I use is closest to the gas burner water heater, so the hot water always hits my bathroom first before any other plumbing in the house. When I moved in, I attached my 2 gal/min. shower head.
I've taken 2 showers since moving in and both have had a problem with temperature regulation. I couldn't get consistent warm water (not scalding hot or cold) for longer than 3 min. at a time. Once I got past 10 min. the frequency of the water changing from anything warm to cold grew. Both times I showered the family was out or at dinner (eating not cooking), so no other water was used while I showered (I did ask).
I talked to my landlord and she said it was lack of pressure. Both showers I had the water running as high flow as was possible, so I didn't think that was valid. Anyway, we tried turning down the temperature on the water heater 4 degrees, hoping that would help. All that did was keep it from getting scaldingly hot 3 out of the 4 times the water switched back to hot in the 2nd shower.
I was thinking the regulator or mixing valve are blocked, eroded or broken. What would you suggest to solve this issue?