Using a heater and a toaster oven together, both about 1500w each, trips the breaker. It seems both are on the same circuit. Moving either appliance to a different location is not really an option. Can an electrician do something so that this load can be handled? I want to get an idea of his work.. what will he do?
Yes an electrician can fix this. I would suggest a second 20a circuit be pulled in. Since you said toaster oven (in a kitchen) there should be 2 20 amp circuits for the small appliances already. 3000w / 120v= 25 amps so you really don’t have many options as you are limited to 20 amp circuits. Depending on the type of service panel and if it has space may really affect the cost ( and access to an attic or crawl space to pull the new circuit). You should be able to get a quote on the job that explains the scope of work , new circuit, number of boxes and outlets ect.
Why run the heater if the toaster oven is on?
When the toaster oven is on, it also is putting 1500W of heat (about 4000 BTU) into the room. Therefore it is redundant to the heater, and you don't need the heater at those times. You can turn it off.
Someone raised an issue about toaster oven heat being delayed heat. Since your other heater is a radiator type, it is also delayed about the same. So shutting off the heater while toasting is a good plan that will yield about the same heat in the room.
Improving service means running new cables to the service panel.
The electrician will cheerfully take your money to run 1 circuit on 1 cable.
However, the lion's share of cost will be labor of fishing cables through the walls. That labor is unaffected by whether 1 cable is run, or 4. So there's big economical savings in running as many as 4 additional circuits on 4 cables (provided you have the circuit breaker space) for barely more than the cost of cables and outlets.
There is also a way to run 2 circuits per cable, however it is largely obsolete and requires compromises.
If this is a kitchen, there is no such thing as too many circuits in a kitchen. Code now requires 2 complete 20A circuits merely for kitchen countertop receptacles. Practicality calls for a dedicated non-GFCI circuit for the fridge. You can't have too many.
Think about a circuit dedicated to heating
If you're running a new circuit anyway, you'll get far more heat capacity by running a 240V circuit. This allows up to 3840 watts of heating per circuit instead of 1500. Further, it allows (requires) you to use installed heaters actually made for, and safe for, permanent/continuous service. Cost for the heaters is very minimal, at $50 for a 2000W Cadet, and that's comparable to a radiator style heater and cheaper-by-the-year than those cheapie 1500W heater-fans. And worlds safer!
And you can run two of them on a 20A/240V circuit. Resistive heating is cheap. To buy.
Kitchen circuits have been required to be 20A for a long time, your capacity then is 120 Volts x 20 Amps = 2400 Watts. If you reduce the heater to 900 or 600 watts then it should not trip. If it does then your breaker is likely failing and replacing it may help. However you may actually find more devices on the same circuit, even the fridge is allowed to be on the same circuit as countertop receptacles.
Sometimes people state that a circuit should not be loaded more than 80%, this is generally conservative and safe advice, but the NEC only restricts 80% on motors and circuits that operate at full current for 3 hours or longer, which both the toaster and heater should be cycling loads.
Otherwise routing another cable or two from the panel is the only option, this could take 2 hours, it could take 22.
Bear in mind your general purpose receptacle circuits were not designed to replace an engineered heating system. Constantly using general purpose in that manner will certainly result in shortened lifespan of some of electrical system components.
The only thing that can be done will involve running a new wire, which is typically a more expensive job (compared to just switching out some light switches or an outlet). There might be a shortcut that can be taken depending on how nearby circuits are run, but figuring that out would take an on-site electrician anyway.
Go into the bid process assuming that a new wire will need to be run. If there are not any blank spots in your current breaker panel, that will make the job a little more expensive if you can use "double" breakers, or a lot more expensive if you need a second electrical panel.
What you can't do is just replace the breaker, because the breaker is limited by the wire size. Even if you happened to have wire rated for a 20A circuit, that still is not enough to power two 1500w appliances.