Diagnosis
You're right to be cautious. The main goal is to clear dust from the air intake and output paths without damaging the fragile ceramic heating element or the fan blades. It doesn't need internal disassembly for routine cleaning.
How to Fix It
Unplug and let it cool. 1) Use a vacuum cleaner with a brush attachment on both the rear (intake) and front (output) metal grilles. Go over them thoroughly—this is 90% of the job. 2) For deeper dust, use a can of compressed air. Hold the heater upright and shoot short bursts through the rear grille to blow dust out the front. Do this outside or over a trash can. 3) Wipe the exterior with a slightly damp cloth, then dry it. Never use liquids, sprays, or immerse any part.
If That Didn't Work
If performance is still poor after vacuuming, there's a chance dust is matted on the heating element itself. This requires removing the rear cover (a few screws). Once open, you can gently use the compressed air to blow dust off the ceramic element blocks. Do NOT touch or wipe the element—it's very brittle.
Heads Up
The most fragile part is the PTC ceramic heating element. Never poke anything through the grilles to clean it. Also, avoid tilting or shaking the heater aggressively to dislodge dust—you can damage the fan balance or the tip-over switch. A quick vacuum every few weeks during use keeps it running efficiently.