Yes, but it may cause more problems than it cures if you have a late model vehicle. Before emission controls and computerized engine controls came along, it was a common practice to install a cooler (160 to 180 degree F.) thermostat for summer driving. The lower thermostat lowered the engine's operating temperature, which in turn reduced the load on the cooling system and reduced the danger of overheating during hot weather driving or when towing a trailer.
It was also common practice to again replace the thermostat come fall and install one with a higher (190 to 195 degrees F.) temperature rating. This would raise the engine's operating temperature so the heater would put out more warm air on a cold winter morning.
This practice is no longer recommended because today's computerized engine control systems require a constant year-round operating temperature of about 195 degrees F.. The engine's emission controls as well as it's fuel and spark control systems are all calibrated to work within a given temperature range. If someone replaced the thermostat with the wrong one for the application (either colder or hotter), it can cause driveability, fuel economy, performance and emissions problems. So if the thermostat is replaced for any reason, it must be replaced with one that has the same (or correct) temperature rating for your vehicle.
Coolant temperature is used for a variety of engine and emission control functions. The coolant sensor on late model engines tells the computer when the engine has reached normal operating temperature. This, in turn, affects fuel enrichment, spark timing, operation of the EGR valve, purging of the charcoal canister, etc. Even on many non-computer engines, thermal vacuum switches (TVS) that react to a specific coolant temperature are used to open and close various vacuum circuits that regulate fuel enrichment, timing and emissions.
If a colder thermostat is installed, the coolant may never get hot enough to trigger the appropriate control functions in the computer or TVS vacuum circuits. As a result the engine will run as if it were continually cold, which increases both fuel consumption and emissions. Too low an operating temperature also increases cylinder wear.
CAUTION: Under no circumstances should an engine be driven without a thermostat! This can produce thermal stress that may crack a head or block!
What about a hotter thermostat? A hotter than normal thermostat in a late model computer controlled engine may activate some control functions too quickly or out of sequence with other control devices (timer delays, etc.) --which could also have an adverse effect on driveability, fuel economy, performance and emissions.