Oh, there's lots ofexpensive lab equipment that could(and needs to be) be home-made cheaply.
How about a good, stong magnetic stirrer/hotplate combo?
I'll stick to the hotplate part here, but just so you know you can procure some incredibly strong magnets just by dissecting a dead computer disk drive...
Most hotplates use a simple on/off thermostat that senses temperature and turns on the heat full-power until it's up to temp then shuts off until the next low-temp switch-on is indicated. This produces frequent cycling which can result in uneven (varying) temperatures which can make it hard to determine if a chemical reaction has been at the proper temperature for the proper amount of time. It can also cause a too-high temperature (a bad thing with some touchy reactions) by shutting off at temperture x-degrees, but the residual heat in the heating element keeps heating the beaker or whatever a bit beyond the set temp. The steadiness of temperature is quite a bit dependent on the "thermal mass" of the heating element and to a lesser extent the item being heated;- something that has a lot of "thermal mass" like an oil bath or thick ceramic heating element will take a long time to heat up /cool down whereas say, a small beaker of liquid or simple electric coil will heat & cool quickly.
My idea is to have a variable voltage to try and keep the temperature constant rather than just using on/off switching , as well as an anticipator for heating things with a large thermal mass without overheating them. (The thermal mass of the heating device is the most important parameter here, lower being better so it reacts to power changes faster, but the thermal mass of the heated object comes into play too. In that case a higher mass is better. This is why water or oil baths are often used in lab experiments heated with a hot plate rather than a variac-controlled heating mantle.)
Anticipators are used in home heating thermostats and are adjusted for the type of heating system in use. For example hydronic (pumped water) baseboard heaters get hot & cool off very quickly, so ther thermostat's anticipator can be set to turn off the boiler/pump only a degreee or so before the set temperature is reached. On the other hand, cast iron radiators in a steam-heat system will radiate heat for quite a while after the boiler is turned off so the anticipator shuts the system down a few degrees earlier. Cast-iron radiator systems that use hot water (water has a large thermal mass) rather than steam will shut down even earlier. Gravity-circulated (rather than pumped) cast iron radiator/water systems will shut down yet a couple of degrees sooner than that.
You get the idea.
Ideally there should be a way to utilize an external temperature sensor so the temperature of the thing being heated, rather than the temperature of the heating device can be measured.
In a more advanced design, a simple programmable device (e.g. an Arduino) could be used to vary the voltage to the heating element, so after several regular heating on/off cycles it could roughly compute the heat loss rate and set the voltage to the heater to keep a constant temperature without having to switch on and off.
Hope this gives you some ideas!