That could be, but it shouldn't lose that much heat, even if the plastic is thin. But I've never used a plastic shelf... However, I think that if you continue to have problems and we've ruled everything else out, you should get a piece of melamine or some similar type of thicker material/board cut to the size of your shelf and put your heat tape and tub on that instead of the shelf. Maybe that can create more insulation for your heat tape. If your room is pretty chilly, it could have a harder time keeping your temp up. Also, perhaps your heat tape is getting hot enough and switching the thermostat off before the inside of your actual tub gets to temp, but again you shouldn't have to set it so high just to get your tub hot enough. Is your temp gun accurate, by chance? If the tub hot spot feels warm to the touch, that sounds like higher than 86 degrees, also.
You're welcome - I hope we get this sorted out!
P.S. My probe is on the shelf right in front of the heat tape, within 1/8", between the back of the tub and the heat tape....