Yes, a dirty cabin/pollen filter will restrict the ac/heater fan output.
the heater matrix is blocked
First you have to see if your blower motor is working or not. If it is and still you have no heat then your heater-core is blocked and needs to be replaced.
If the blower is good then the problem is coolant. Something is stopping the warm coolant from the engine from reaching the heater core inside the car. This might be thermostat, heater control valve, blocked heater hose or a blocked heater core. I would suggest letting the car warm up and checking the heater hoses (2) by hand to see where the hot water stops. If there is no hot water at all it is probably a thermostat problem.
Check that the pollen filter has been replaced. Check that the heater fan hasn't seized due to water logging after pollen filter becomes blocked. Check resistor is working (next to heater fan on firewall) Check relay is working correctly.
It could be a partially blocked heater core or AC evaporator, or it could be a lot of buildup on the fan. Check if there is a filter after the fan, under the dash or behind glove box, It is clogged, shake it out, and or wash it.
Remove the wiring harness from the back of your 2005 Chevy Cavalier heater blower motor. Remove the heater blower motor retaining bolts. Remove the heater blower fan.
This could be due to the filter being blocked or the hot water heater outlet may be slightly blocked and also check your aerators to your hot water taps
Heater blower resistor is what controls the low medium high speeds...
No, I have a 1998 Cavalier and it does not have a cabin filter. You can take off the 3 bolts off the heater blower and remove any leaves or debris.
under your wipers is a the cover for the cabin air filter. under that is your blower simple removal and replace but the blower isn't cheap new
The blower may simply have burned out. If the blower is out then the heater probably still works.
Remove the wiring harness to the heater blower fan. Remove the retaining bolts. Remove the fan from the blower. Reverse the process to install the new heater blower fan.