I keep getting screwed over by people using the Heartbeat Sensor attachment. I was wondering - is there is a way that I can avoid showing up on it or otherwise disable it?
The Assassin perk keeps you off of enemy heartbeat sensors, thermal scopes, and UAV. The pro version also gives you immunity to EMP and Counter-UAV, and makes it so that your name and red crosshairs don't show up if an enemy has you in their sights.
I'll also add that EMP grenades and the EMP killstreak reward disable enemy heartbeat sensors, but only for the duration of the EMP effect.
I would add - from a strategic standpoint you should adjust when you see the enemy is using heartbeat. If you do as @agent86 suggests and switch to a counter-heartbeat perk, item or killstreak, then try and protect campers on your team. You will be invisible, and the campers will draw their attention. If you don't opt for assassin, don't camp - or at least expect that each time you camp the enemy will focus on you and be prepared.
This same strategy applies to UAVs and other air support. When you know the enemy can see you, prepare yourself. When you know they see your allies but not you (like when you're using Blind Eye) - then support vulnerable campers who will be targets.