For a short term need where you'll turn on the heater when you need it and turn it off again shortly afterwards, you're probably going to be best off with some form of radiant heat. This type of heater will emit most of its heat as infrared radiation that you can direct toward wherever you're standing.
A typical radiant heater will have ceramic coated or metal coils (such as you would find inside a toaster or toaster oven) with a reflective surface behind that lets you direct the heat.
Some examples:
There are also in-floor (also in-ceiling or in-wall) radiant heaters that work similarly, but they require installation and more warm-up time before they will warm you.
You can also find heat lamps that fit in a standard light fixture that are designed to project radiant heat -- these are typically found in bathrooms to help warm the floor and yourself after a shower.
All heaters give off radiant heat to some degree, but radiant heaters are optimized to provide radiant heat that you can direct.
The advantage of a radiant heater is that it provides immediate heat that you can direct to exactly where you'll be standing and it can save energy since it doesn't need to heat the entire room when you only need heat for a short time. The disadvantage is that without heating the entire room, the radiant heat will only be felt on the parts of your body that are exposed to it, so, for example, if the heater was sitting on the counter (which I wouldn't recommend for safety reasons) and aimed at your face, you wouldn't feel the heat at your feet and the floor and other surfaces would still feel cold.
Keep in mind that any heater will use a significant amount of power (1500W is typical), so if you are planning on using any other small kitchen appliances at the same time (Toaster, Microwave oven, etc) and it's plugged into the same circuit as the heater, you might exceed the capacity of the circuit.
And, as with any heat generating appliance, operating it safely is important - don't put it where it can be easily knocked over or where pets or children can get close to it. Keep combustibles a safe distance from the heater (the instruction manual will have guidelines). Modern units will have tip-over and over-heat sensors, so avoid heaters of unknown age such as you might find at a garage sale.
We inherited a a hot tub with a house purchase, it was probably 10 years old. After a few months of use, it would sometimes trip the GFCI breaker during use.
I opened the access panel on the hot tub and opened up the control box and the heater unit itself had some corrosion hear the pressure switch.
I removed the corroded heater and replaced it with an aftermarket heater, like the one below. This solved my GFCI problem. FYI, you'd need to buy the pressure switch separately, heavy gauge wire, and be comfortable installing such a device yourself. Or, buy it and hire an electrician to install it.
Best Answer
If your carbon monoxide alarm is going off, you need to assume that there's actually carbon monoxide in dangerous levels in that area. If the heater is electric it probably shouldn't be emitting CO but maybe there's a manufacturing defect that's causing the heating element or plastic to burn.
CO is lethal and totally undetectable by people, so if the alarm goes off you need to leave the building and open the windows. The absence of smoke does not mean that you are safe.
(CO detectors have a limited lifespan: 2-10 years, depending on the model. There should be a date stamped on it somewhere. If it's at "retirement" age you should probably replace it anyway, and then you can see if the new one still goes off.)
Revision based on question update:
You must not ignore the CO detector. People can and do die in their own homes of CO poisoning, oblivious to the problem. Unlike smoke/fire, there's no way for you to tell the source of the problem or evaluate its severity, and no way to tell if the problem has been resolved. You probably have a sub-standard or defective heater — I would not use it anymore.