When the smell persists for weeks on end, there is something wrong, plus it needs to be checked suddenly, and usually, this smell is caused when the dust plus dirt accumulated in the boiler over time burns.
It is not unofficial for the boiler to have unusual smells, however one of the most official smells is a burning substance, especially after a long stage of disuse, then dust plus dirt often accumulate on the boiler when it is not used during Summer plus other warmer months when heating is not a priority, in such cases, the boiler may produce some burning smell when worked on for the first time after a long time, however this smell may linger a few hours or even nights but will eventually go away… However, it should be spine-chilling if the burning smell persists a few weeks on. Most of the surface debris plus dust will be combusted within hours, plus at maximum accumulation, at least a few nights should do. When the smell persists for weeks on end, there is something wrong, plus it needs to be checked suddenly, and usually, this smell is caused when the dust plus dirt accumulated in the boiler over time burns. Typically, the scent is light plus promptly dissipates since it is nothing major. If it persists, then there is a possibility that something larger was trapped inside the boiler without your knowledge, however small pets, brooms, brushes, plus sporadically knitted items find their way into the boiler when it is not in use, however you should constantly check the reachable parts of your boiler every time before you light up the boiler. If you suspect that something is trapped inside the boiler plus could be the reason for such a smell, then switch it off right away plus contact an Heating, Ventilation & A/C dealer to assist you with the safe extraction of the item. Insisting on having the boiler can cause drastic harm to the boiler, especially if the trapped item is plastic.